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For the following function state the following: its domain, any discontinuities and their types, what values should redefine the function to remove any removable discontinuities (give the extended function).

asked 9 hours ago in Mathematics by TestMaverick Wooden (2,754 points) | 122 views

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What are the different types of discontinuities in calculus?

asked 9 hours ago in Mathematics by TestMaverick Wooden (2,754 points) | 7 views

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Find the points of continuity and discontinuity of the following functions $$ \text { 1. } f(x)=\frac{1}{x^{2}+1} \quad \text { 2. } g(x)=e^{1 / x} $$

asked 9 hours ago in Mathematics by TestMaverick Wooden (2,754 points) | 6 views

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When is a real-valued function continuous?

asked 10 hours ago in Mathematics by TestMaverick Wooden (2,754 points) | 6 views

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Find the limit $\lim _{x \rightarrow \infty} x+e^{-x}$

asked 10 hours ago in Mathematics by TestMaverick Wooden (2,754 points) | 6 views

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Find the limit $\lim _{x \rightarrow \infty} \frac{3 x+1}{|x|+2}$

asked 10 hours ago in Mathematics by TestMaverick Wooden (2,754 points) | 7 views

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Find the limit $\lim _{x \rightarrow \infty} \frac{6 x^{2}-4 x^{5}+7 x-1}{12 x^{5}-3 x^{2}+2}$

asked 10 hours ago in Mathematics by TestMaverick Wooden (2,754 points) | 7 views

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Find the limit $\lim _{x \rightarrow-\infty} \frac{x-9}{2 x-x^{2}}$

asked 10 hours ago in Mathematics by TestMaverick Wooden (2,754 points) | 6 views

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Find the limit $\lim _{x \rightarrow \infty} \frac{x^{3}-6 x+1}{x^{2}+2 x-3}$

asked 10 hours ago in Mathematics by TestMaverick Wooden (2,754 points) | 6 views

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What are horizontal asymptotes when dealing with limits in calculus?

asked 10 hours ago in Mathematics by TestMaverick Wooden (2,754 points) | 7 views

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What is the End Behavior Model?

asked 10 hours ago in Mathematics by TestMaverick Wooden (2,754 points) | 6 views

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How do you define infinite limits in calculus?

asked 10 hours ago in Mathematics by TestMaverick Wooden (2,754 points) | 7 views

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Evaluate the following limit $$ \lim _{\theta \rightarrow 0} \frac{\sin \theta}{\theta} $$

asked 10 hours ago in Mathematics by TestMaverick Wooden (2,754 points) | 7 views

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How does the sandwich/squeeze theorem for limits work?

asked 10 hours ago in Mathematics by TestMaverick Wooden (2,754 points) | 7 views

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How do you explain left and right hand limits in calculus?

asked 10 hours ago in Mathematics by TestMaverick Wooden (2,754 points) | 6 views

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Find the limit of $f(x)$ as $x$ approaches 2 for the following function. $$ f(x)=\left\{\begin{array}{ll} x^{2} & x \neq 2 \\ 0 & x=2 \end{array}\right. $$

asked 10 hours ago in Mathematics by TestMaverick Wooden (2,754 points) | 7 views

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What are some of the properties of limits in calculus?

asked 10 hours ago in Mathematics by TestMaverick Wooden (2,754 points) | 6 views

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In calculus, how are limits defined?

asked 10 hours ago in Mathematics by TestMaverick Wooden (2,754 points) | 7 views

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What are teaching and learning strategies?

asked 13 hours ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 7 views

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What is the multiplicative inverse of 1/16 ÷ 1/81 +-1/8?

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 8 views

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A bag has balls of four colours red, blue, pink,green. Half the total number of balls are pink. One -fourth of the number of green balls equals one third of the number of blue balls.

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 11 views

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Find a and $b$ if $3 \sqrt{7} / 3-\sqrt{7}+3=\sqrt{7} / 3+\sqrt{7}=a+b \sqrt{7}$

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 6 views

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$\left(-9^{*} 24\right)$ divided by $[-15-(23)]$

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 6 views

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if a×b ={(3,2) (3,5) (5,2) (5,4)} then find a and b

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 6 views

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If a, 4a and 6a+5 are in an arithmetic progression. What is the value of a?

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 5 views

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Simplify $(2-\sqrt{\frac{5}{2}}+\sqrt{5})^2 - (2+\sqrt{\frac{5}{2}})^2$

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 6 views

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P, Q, R, S, T and U are six students studying in a class. Each of them has a different height and weight. The tallest is not the heaviest .

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 6 views

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Solve the simultaneous equations: $\frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2$ and $\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1$

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 7 views

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Find the partial fraction decomposition of the following expression: $$ \frac{x^{3}+3}{x^{2}-2 x-3} $$

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 7 views

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What are improper fractions?

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 6 views

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Find the partial fraction decomposition of $\frac{3 x^{4}-2 x^{3}+6 x^{2}-3 x+3}{x^{5}+3 x^{4}+4 x^{3}+12 x^{2}+4 x+12}$.

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 8 views

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What are repeated quadratic factors?

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 5 views

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Find the partial fraction decomposition of the following expression: $$ \frac{6 x^{2}+21 x+11}{x^{3}+5 x^{2}+3 x+15} $$

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 8 views

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What are linear factors?

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 6 views

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What are repeated linear factors?

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 5 views

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What are quadratic factors?

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 5 views

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Find the partial fraction of the following expression: $$ \frac{x^{2}+5 x-6}{x^{3}-7 x^{2}+16 x-12} $$

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 7 views

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Find the partial fraction decomposition of the following expression: $$ \frac{2 x-1}{x^{3}-6 x^{2}+11 x-6} $$

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 9 views

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What are partial fractions of functions?

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 7 views

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What is the definition of $e$, the base of the natural logarithm?

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 7 views

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Using a right-angled triangle how can we derive the trigonometric identity $1+\cot ^{2} \theta=\csc ^{2} \theta$

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 8 views

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How is the unit circle and trig functions?

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 7 views

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Factor the polynomial $x^{5}+x^{4}-2 x^{3}+4 x^{2}-24 x$.

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 8 views

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What are the steps and methods for factoring polynomials?

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 21 views

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What are complex conjugates?

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 5 views

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How are complex numbers related to real numbers?

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 8 views

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Is $f(x)=2 x-x^{2}$ even, odd, or neither?

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 8 views

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When is a mathematical function classified as even?

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 8 views

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Find the inverse function of $$ f(x)=\frac{5 x+2}{4 x-3} $$

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 8 views

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Can the input of one function be the output of another mathematical function?

asked 1 day ago in Mathematics by ♦MathsGee Diamond (75,812 points) | 8 views

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