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Tag
first-order
Recent questions tagged first-order
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Determine the domain of each of the following. \(f(x)=2 x^3+4 x^2+6\)
Determine the domain of each of the following.\(f(x)=2 x^3+4 x^2+6\)
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Compute the definite integral of the following function over the interval \( [0, \pi ] \)
Compute the definite integral of the following function over the interval \( [0, \pi ] \)\[f(x)=\sin ^{2}(x)+\cos ^{2}(x)\]
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Which function, \(f\) or \(g\), has the equation \(y=a^x\) ?
a) Which function, \(f\) or \(g\), has the equation \(y=a^x\) ?b) What is the range of \(g(x)\) ?c) Give the equation of the asymptote of \(g(x)\).d) Give the equation of...
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What is the difference between a first-order optimization algorithm and a second-order optimization algorithm?
What is the difference between a first-order optimization algorithm and a second-order optimization algorithm?
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The domain of the function \(f(x)=\sin ^{-1}\left(\frac{|x|+5}{x^2+1}\right)\) is \((-\infty,-a] \cup[a, \infty)\), Then a is equal to:
The domain of the function \(f(x)=\sin ^{-1}\left(\frac{|x|+5}{x^2+1}\right)\) is \((-\infty,-a] \cup[a, \infty)\), Then a is equal to:(1) \(\frac{1+\sqrt{17}}{2}\)(2) \(...
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If \(|x|<1,|y|<1\) and \(x \neq y\), then the sum to infinity of the following series \((x+y)+\left(x^2+x y+y^2\right)+\left(x^3+x^2 y+\right.\) \(\left.x y^2+y^3\right)+\ldots .\). is :
If \(|x|<1,|y|<1\) and \(x \neq y\), then the sum to infinity of the following series \((x+y)+\left(x^2+x y+y^2\right)+\left(x^3+x^2 y+\right.\) \(\left.x y^2+y^3\right)+...
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If the tangent to the curve \(y=x+\) siny at a point \((a, b)\) is parallel to the line joining \(\left(0, \frac{3}{2}\right)\) and \(\left(\frac{1}{2}, 2\right)\), then
If the tangent to the curve \(y=x+\) siny at a point \((a, b)\) is parallel to the line joining \(\left(0, \frac{3}{2}\right)\) and \(\left(\frac{1}{2}, 2\right)\), then(...
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A line parallel to the straight line \(2 x-y=0\) is tangent to the hyperbola \(\frac{x^2}{4}-\frac{y^2}{2}=1\) at the point \(\left(x_1, y_1\right)\). Then \(x_1^2+5 y_1^2\) is equal to:
A line parallel to the straight line \(2 x-y=0\) is tangent to the hyperbola \(\frac{x^2}{4}-\frac{y^2}{2}=1\) at the point \(\left(x_1, y_1\right)\). Then \(x_1^2+5 y_1^...
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Give an example of a function where \(f^{\prime}(x) \neq 0\) and \(f^{\prime \prime}(x)=\) \(0 .\)
Give an example of a function where \(f^{\prime}(x) \neq 0\) and \(f^{\prime \prime}(x)=\) \(0 .\)
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Give an example of a function \(f(x)\) where \(f^{\prime}(x)=0\).
Give an example of a function \(f(x)\) where \(f^{\prime}(x)=0\).
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Give an example of a function \(f(x)\) where \(f^{\prime}(x)=f(x)\)
Give an example of a function \(f(x)\) where \(f^{\prime}(x)=f(x)\)
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Let \(f(x)=\sin x+2 x+1\). Approximate \(f(3)\) using an appropriate tangent line.
Let \(f(x)=\sin x+2 x+1\). Approximate \(f(3)\) using an appropriate tangent line.
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Experimental Measurements determine that a function \(f(x)\) satisfies \(f(0)=0, f^{\prime}(0)=1\) and \(f(1)=2\).
Experimental Measurements determine that a function \(f(x)\) satisfies \(f(0)=0, f^{\prime}(0)=1\) and \(f(1)=2\).(a) Estimate \(f(1 / 3)\) using tangent line (linear) ap...
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If \(h(x)=f^{2}(x)-g^{2}(x), f^{\prime}(x)=-g(x)\) and \(g^{\prime}(x)=f(x)\), then \(h^{\prime}(x)\) is:
If \(h(x)=f^{2}(x)-g^{2}(x), f^{\prime}(x)=-g(x)\) and \(g^{\prime}(x)=f(x)\), then \(h^{\prime}(x)\) is:A) 0B 1C) \(-4 f(x) g(x)\)D) \((-g(x))^{2}-(f(x))^{2}\)
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How many square units are in the region satisfying the inequalities \(y \geq|x|\) and \(y \leq-|x|+3\) ? Express your answer as a decimal.
How many square units are in the region satisfying the inequalities \(y \geq|x|\) and \(y \leq-|x|+3\) ? Express your answer as a decimal.
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What is the domain of the function \[ f(x)=\frac{(2 x-3)(2 x+5)}{(3 x-9)(3 x+6)} ? \] Express your answer as an interval or as a union of intervals.
What is the domain of the function\[f(x)=\frac{(2 x-3)(2 x+5)}{(3 x-9)(3 x+6)} ?\]Express your answer as an interval or as a union of intervals.
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For every \(a, b, b \neq a\) prove that \[ \frac{a^{2}+b^{2}}{2}>\left(\frac{a+b}{2}\right)^{2} . \]
For every \(a, b, b \neq a\) prove that\[\frac{a^{2}+b^{2}}{2}>\left(\frac{a+b}{2}\right)^{2} .\]
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Put \(f(0,0)=0\), and \[ f(x, y)=\frac{x y\left(x^{2}-y^{2}\right)}{x^{2}+y^{2}} \]
Put \(f(0,0)=0\), and\[f(x, y)=\frac{x y\left(x^{2}-y^{2}\right)}{x^{2}+y^{2}}\]if \((x, y) \neq(0,0)\). Prove that(a) \(f, D_{1} f\), and \(D_{2} f\) are continuous in \...
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If \(f(0,0)=0\) and \[ f(x, y)=\frac{x y}{x^{2}+y^{2}} \quad \text { if }(x, y) \neq(0,0) \] prove that \(\left(D_{1} f\right)(x, y)\) and
If \(f(0,0)=0\) and\[f(x, y)=\frac{x y}{x^{2}+y^{2}} \quad \text { if }(x, y) \neq(0,0)\]prove that \(\left(D_{1} f\right)(x, y)\) and \(\left(D_{2} f\right)(x, y)\) exis...
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Describe the connection with the solution of the initial value problem of the differential equation
Calculate\[\exp \left(t x^{3} \frac{d}{d x}\right) x\]All terms must be summed up. Describe the connection with the solution of the initial value problem of the different...
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250
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Show that the homogeneous equation \[ \frac{d u}{d x}+f\left(\frac{u}{x}\right)=0 \] is transformed by
Show that the homogeneous equation\[\frac{d u}{d x}+f\left(\frac{u}{x}\right)=0\]is transformed by\[y=x, \quad v(y(x))=\frac{u(x)}{x}\]into the separable equation\[v+y \f...
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260
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Solve for \(x\) in \(\dfrac{x+1}{2}+4=7\)
Solve for \(x\) in \(\dfrac{x+1}{2}+4=7\)
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Solve for \(x\) in \(\frac{1}{x-4}+\frac{2}{x^{2}-16}=\frac{3}{x+4}\)
Solve for \(x\) in \(\frac{1}{x-4}+\frac{2}{x^{2}-16}=\frac{3}{x+4}\)
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For the next problem with the production line diagnosed as being due to an initial repair that was incomplete, what is the probability that this initial repair was made by Janet?
Four technicians regularly make repairs when breakdowns occur on an automated production line. Janet, who services \(20 \%\) of the breakdowns, makes an incomplete repair...
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A function \(f(x, y)\) is continuous at a point \((a, b)\) if
A function \(f(x, y)\) is continuous at a point \((a, b)\) if
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With \(a<b\), the total variation of \(f(x)\) on a finite or infinite interval \((a, b)\) is
With \(a<b\), the total variation of \(f(x)\) on a finite or infinite interval \((a, b)\) is
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Give an example of a quadratic function of the form \(f(x)=x^{2}+b x+c\) whose tangent line is \(y=3 x+1\) at the point \((0,1)\).
Give an example of a quadratic function of the form \(f(x)=x^{2}+b x+c\) whose tangent line is \(y=3 x+1\) at the point \((0,1)\).
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Give an example of a function that satisfies \(f(-1)=0, f(10=0\), and \(f^{\prime}(x)>0\) for all \(x\) in the domain of \(f^{\prime}\).
Give an example of a function that satisfies \(f(-1)=0, f(10=0\), and \(f^{\prime}(x)>0\) for all \(x\) in the domain of \(f^{\prime}\).
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Give the expression for \(A(t)\), the value of the investment in CAD after \(t\) years if the interest is compounded continuously by writing down the differential equation that \(A\) satisfies and solving it.
An amount of \(A_{0}\) CAD is invested against yearly interest of \(p \%\). Give the expression for \(A(t)\), the value of the investment in CAD after \(t\) years if the ...
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By looking at an initial value problem $d y / d x=f(x, y)$ with $y\left(x_{0}\right)=y_{0}$, it is not always possible to determine the domain of the solution $y(x)$ or the interval over which the function $y(x)$ satisfies the differential equation.
Interval of definition. By looking at an initial value problem $d y / d x=f(x, y)$ with $y\left(x_{0}\right)=y_{0}$, it is not always possible to determine the domain of ...
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If $f(x)=x+\sqrt{x^{2}+1}+\frac{1}{x-\sqrt{x^{2}+1}}$, what is the value of $f\left(2016^{2017}\right) ?$
If $f(x)=x+\sqrt{x^{2}+1}+\frac{1}{x-\sqrt{x^{2}+1}}$, what is the value of $f\left(2016^{2017}\right) ?$
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Solve \$ 2,500(1+0.06 t)+\$1,000(1+0.04 t)= \$3,553.62
Solve \$ 2,500(1+0.06 t)+\$1,000(1+0.04 t)= \$3,553.62
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Solve for $x$ in $\frac{5}{x}+\frac{1}{x}=\frac{2}{x}+2$
Solve for $x$ in $\dfrac{5}{x}+\dfrac{1}{x}=\dfrac{2}{x}+2$
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If $h(x)=f^{2}(x)-g^{2}(x), f^{\prime}(x)=-g(x)$ and $g^{\prime}(x)=f(x)$, then $h^{\prime}(x)$ is:
If $h(x)=f^{2}(x)-g^{2}(x), f^{\prime}(x)=-g(x)$ and $g^{\prime}(x)=f(x)$, then $h^{\prime}(x)$ is:
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Which of the following answers choices is a solution to the differential equation $y^{\prime \prime \prime}-6 y^{\prime \prime}+11 y^{\prime}-6 y=0 ?$
Which of the following answers choices is a solution to the differential equation $y^{\prime \prime \prime}-6 y^{\prime \prime}+11 y^{\prime}-6 y=0 ?$
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If $h(x)=2 x \cdot \cos x$, find $h^{\prime \prime}(\pi)$
If $h(x)=2 x \cdot \cos x$, find $h^{\prime \prime}(\pi)$
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Solve for $x$ : $\quad 2^{x}=\frac{1}{16}$
Solve for $x$ : $\quad 2^{x}=\dfrac{1}{16}$
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Let $f(x)=-2 x^{2}+1$ and $g(x)=4 x-3$. Find $(f \circ g)(x)$.
Let $f(x)=-2 x^{2}+1$ and $g(x)=4 x-3$. Find $(f \circ g)(x)$.
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Let $f(x)=3 x^{2}-1$ and $g(x)=-2 x+7$. Find $(f+g)(-3)$.
Let $f(x)=3 x^{2}-1$ and $g(x)=-2 x+7$. Find $(f+g)(-3)$.
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Simplify: $ \frac{2}{x^{2}-x}+\frac{x^{2}+x+1}{x^{3}-1}-\frac{x}{x^{2}-1} $
Simplify:$$\frac{2}{x^{2}-x}+\frac{x^{2}+x+1}{x^{3}-1}-\frac{x}{x^{2}-1}, \quad(x \neq 0 ; x \neq \pm 1)$$
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Simplify: $ \frac{x-2}{x^{2}-4}+\frac{x^{2}}{x-2}-\frac{x^{3}+x-4}{x^{2}-4}, \quad(x \neq \pm 2) $
Simplify:$$\frac{x-2}{x^{2}-4}+\frac{x^{2}}{x-2}-\frac{x^{3}+x-4}{x^{2}-4}, \quad(x \neq \pm 2)$$
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Simplify: $ \frac{x^{2}-x-2}{x^{2}-4} \div \frac{x^{2}+x}{x^{2}+2 x}, \quad(x \neq 0 ; x \neq \pm 2) $
Simplify:$$\frac{x^{2}-x-2}{x^{2}-4} \div \frac{x^{2}+x}{x^{2}+2 x}, \quad(x \neq 0 ; x \neq \pm 2)$$
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Solve for $r$ in the equation: $V=\pi r^{2} h(r>0)$
Solve for $r$ in the equation: $V=\pi r^{2} h(r>0)$
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May 19, 2021
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Solve for $x$ in $\frac{3 x-2}{2}=x+1$
Solve for $x$ in $\frac{3 x-2}{2}=x+1$
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Let $f(x)=2 x+\cos x$. Say why $f(x)$ is an increasing function for all $x$. Let $g(x)=f^{-1}(x)$, and calculate $g^{\prime}(0)$.
Let $f(x)=2 x+\cos x$. Say why $f(x)$ is an increasing function for all $x$. Let $g(x)=f^{-1}(x)$, and calculate $g^{\prime}(0)$.
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Let $f(x)=x^{2} \sin \left(\frac{1}{x}\right)$ if $x \neq 0$, and $f(0)=0 .$ Find $f^{\prime}(0)$ (or say why it doesn't exist.)
Let $f(x)=x^{2} \sin \left(\frac{1}{x}\right)$ if $x \neq 0$, and $f(0)=0 .$ Find $f^{\prime}(0)$ (or say why it doesn't exist.)
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Convert $\frac{d^{3} x}{d t^{3}}+x=0$ to a first-order differential equation. Solve this equation over the interval $[0,1]$ for the initial conditions $x^{\prime \prime}(0)=0, x^{\prime}(0)=1$, and $x(0)=0$.
Convert $\frac{d^{3} x}{d t^{3}}+x=0$ to a first-order differential equation. Solve this equation over the interval $[0,1]$ for the initial conditions $x^{\prime \prime}(...
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convert
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Convert $\frac{d^{2} x}{d t^{2}}+x=0$ to a first-order differential equation. Solve over the interval $[0, \pi]$ with $h=\frac{\pi}{10}$ assuming the initial conditions $x(0)=1$ and $x^{\prime}(0)=0$.
Convert $\frac{d^{2} x}{d t^{2}}+x=0$ to a first-order differential equation. Solve over the interval $[0, \pi]$ with $h=\frac{\pi}{10}$ assuming the initial conditions $...
MathsGee
Platinum
113k
points
MathsGee
asked
May 9, 2021
Mathematics
convert
first-order
differential
equation
solve
interval
initial-conditions
+
–
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