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Differentiate \(k(t)=\frac{(t+2)^{3}}{\sqrt{t}}\) with respect to \(t\)
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Differentiate \(g(t)=4(t+1)^{2}(t-3)\) with respect to \(t\)
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Differentiate the function \(y=3 x^{5}\)
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The function $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ is
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The function $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ isThe function $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ is   A. strictly increasing on $(-\infty, \infty)$,   B. strictly increasing on $(-\infty ...
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The function $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ has ...
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The function $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ has ...The function $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ has   A. no point of inflection and is concave up on $(-\infty, \infty)$,   B. no point o ...
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Sketch the graph of $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$
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Sketch the graph of $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$Sketch the graph of $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ ...
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Let $x^{2}+2 x \arctan y=y \cos x$. Find $y^{\prime}$ at $\left(\dfrac{\pi}{2},-1\right)$.
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Evaluate the integral: $\int \dfrac{3 x+2}{\sqrt{4-3 x^{2}}} d x$
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Evaluate the integral: $\int \dfrac{3 x+2}{\sqrt{4-3 x^{2}}} d x$Evaluate the integral:   $\int \dfrac{3 x+2}{\sqrt{4-3 x^{2}}} d x$ ...
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Evaluate the integral: $\int_{0}^{\pi} 2 x \cos 2 x d x$
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Find the local extrema of $f(x)=\cot x+\ln \sin ^{4} x$ on $(0, \pi)$.
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Find the local extrema of $f(x)=\cot x+\ln \sin ^{4} x$ on $(0, \pi)$.Find the local extrema of $f(x)=\cot x+\ln \sin ^{4} x$ on $(0, \pi)$. ...
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Which of the following statements is NOT TRUE?
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Which of the following statements is NOT TRUE?Which of the following statements is NOT TRUE?   (A) $\int_{0}^{3} \frac{1}{(x-4)^{2}} d x=\frac{3}{4}$. (B) $\int_{0}^{3} \frac{1}{(x-4)^{2}} ...
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Evaluate $\int \dfrac{\ln z}{(1+z)^{2}} d z$
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Evaluate the following integral: $\int \frac{t}{\sqrt{t^{4}-1}} d t$.
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Evaluate the following integral: $\int \frac{t}{\sqrt{t^{4}-1}} d t$. Evaluate the following integral: $\int \dfrac{t}{\sqrt{t^{4}-1}} d t$. Hint: You may use the fact that $\int \sec \theta d \theta=\ln |\sec ...
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asked in Mathematics Jan 13
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Evaluate the integral $\int_{1}^{2} \dfrac{2 s-2}{\sqrt{-s^{2}+2 s+3}} d s$
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Evaluate $\int \dfrac{1}{\left(1+x^{2}\right) \arctan x} d x$
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Determine whether the integral $\int_{0}^{1} \dfrac{1}{\left(1+x^{2}\right) \arctan x} d x$ is convergent or divergent.
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Evaluate $\int_{-1}^{2} \dfrac{x}{\sqrt{10+2 x+x^{2}}} d x=$
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Evaluate $\int_{-1}^{2} \dfrac{x}{\sqrt{10+2 x+x^{2}}} d x=$Evaluate $\int_{-1}^{2} \dfrac{x}{\sqrt{10+2 x+x^{2}}} d x=$     A. $\quad 3(1-\sqrt{2})-\ln (1+\sqrt{2})$   B. $3(\sqrt{2}-1)-\ln ...
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asked in Mathematics Jan 13
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Evaluate $\int_{1}^{2} \frac{x^{2}-x+4}{(x+1)\left(x^{2}+1\right)} d x=$
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Evaluate $\int_{1}^{2} \frac{x^{2}-x+4}{(x+1)\left(x^{2}+1\right)} d x=$Evaluate $\int_{1}^{2} \dfrac{x^{2}-x+4}{(x+1)\left(x^{2}+1\right)} d x=$   A. $\quad \ln \left(\frac{27}{20}\right)+\arctan 2-\frac{\pi}{4}$ ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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Evaluate $\int_{0}^{\pi / 4} \sin 3 x \cos 5 x d x=$
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Evaluate $\int_{0}^{\pi / 4} \sin 3 x \cos 5 x d x=$Evaluate $\int_{0}^{\pi / 4} \sin 3 x \cos 5 x d x=$   A. $\frac{1}{2}$   B. $-\frac{1}{2}$   C. $\frac{1}{4}$   D. $-\fra ...
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asked in Mathematics Jan 13
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Evaluate $\int_{0}^{\infty} \frac{4}{x^{2}+2} d x=$
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Evaluate $\int_{0}^{\infty} \frac{4}{x^{2}+2} d x=$Evaluate $\int_{0}^{\infty} \frac{4}{x^{2}+2} d x=$   A. $-\frac{\pi}{\sqrt{2}}$   B. $\quad \sqrt{2} \pi$   C. $\frac{\pi}{\sqrt ...
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asked in Mathematics Jan 13
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What is the most suitable substitution to use to solve the integral $\int \frac{1}{\sqrt{t^{2}-81}} d t ?$
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What is the most suitable substitution to use to solve the integral $\int \frac{1}{\sqrt{t^{2}-81}} d t ?$What is the most suitable substitution to use to solve the integral $\int \frac{1}{\sqrt{t^{2}-81}} d t ?$   A) $t=9 \sec \theta$.   B) ...
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asked in Mathematics Jan 13
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The derivative with respect to $x$ of $\int_{\frac{\pi}{7}}^{x} e^{t^{2}} \operatorname{cosec}(t) d t$ is
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The derivative with respect to $x$ of $\int_{\frac{\pi}{7}}^{x} e^{t^{2}} \operatorname{cosec}(t) d t$ isThe derivative with respect to $x$ of $\int_{\frac{\pi}{7}}^{x} e^{t^{2}} \operatorname{cosec}(t) d t$ is   A) $e^{x^{2}} \operatorname{cosec}( ...
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asked in Mathematics Jan 13
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Find $\frac{d}{d x}\left(x \int_{2}^{x^{2}} \frac{1}{9+t^{2}} d t\right)$
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Determine whether the integral $\int_{3}^{3+e} \ln (x-3) d x$ is convergent or divergent. If convergent, give the value the integral converges to.

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