12.6+OFSA

OFSA for Limits

This page contains peer generated questions that help you assess your understanding. Remember that questions may not represent the rigor of the questions you may be expected to complete on formal assessments. This page is simply an OFSA - opportunity for self assessment.

= __**Question 1**__ =

toc Given math f(x)=3x^2-5x math evaluate math \lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}h math

A. 6x+3h-5 B. 6x-5 C. 0 D. Does Not Exist (DNE)

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=__Question 2__=

Evaluate math \lim_{n \to -\infty }\frac{x+9}{4x+5} math

A. 1/4 B. 1 C. 2/5 D. Indeterminant

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=__**Question 3**__=

Find the value of A that makes math \[f(x) = \begin{cases} \(1-2x) & \text{ if } x\leq -2 & (Ax+5) & \text{ if } x>-2 \end{cases}

\] math continuous.

A. f(a) does not exist, so therefore the function is not continuous B. 5 C. Undefined D. 0

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=__**Question 4**__= math Find: \lim_{x\rightarrow 0} \frac{(3+x)^2 - 9}{x} math a. Limit Does Not Exist b. -6 c. -9 d. 6

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=__**Question 5**__= math Find: \lim_{x\rightarrow 0} \frac{\sqrt{x^2+9}- 3}{x^2} math a. Limit Does Not Exist b.

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=__**Question 6**__= math Let: \[f(x) = \begin{cases}

\sqrt{x - 4}

& \text{ if } x> 4

& 8-2x

& \text{ if } x < 4

\end{cases} \] math

Determine whether

math \lim_{x\rightarrow 4} f(x) exists. math Click here for solution.

=__**Question 7**__= Find the derivative of the equation: f(x) math Let f(x) = \sqrt{x} math (a) Find f'(a) (b) Find f'(1), f'(4), and f'(9)

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=__**Question 8**__= math Find: \lim_{x\rightarrow 3} (2x^3 - 10x -8) math a. Limit Does Not Exist b. -20 c. 16 d. 32

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=__**Question 9**__= math Find: \lim_{x\rightarrow -1} \frac{x^2 + 5x}{x^4 + 2} math a. Limit Does Not Exist b. -4/3 c. 2 d. 6

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=__**Question 10**__= math Find: \lim_{x\rightarrow 1} \frac{x-1}{x^2 - 1} math a. Limit Does Not Exist b. 0 c. 1/2 d. 2

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=__**Question 11**__= math Find: \lim_{x\rightarrow} \frac{x^{2}+2x-3}{x^{2}-1} math a. DNE b. 0 c. 2 d. 1/2

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=__**Question 12**__= math Find: \lim_{x\rightarrow 3}\tfrac{\sqrt{x+1}}{x^{2}-1} math a. 0 b. DNE c. 1/4 d. 2

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=__**Question 13**__= math \lim_{x\to \infty } \frac {x^{3}+4x-3}{x^{3}+2} math a. 1 b. -3/2
 * c. DNE**
 * d. 2/3**

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=__**Question 14**__= Determine for which values of "a" f(x) would be a continuous function. math f(x)= \left\{\begin{matrix} ax^2+3\rightarrow x< 4 \\ \sqrt{x}+10\rightarrow x\geq 4 \end{matrix}\right. math

a.13 b. 15/16 c. 9/16 d. Never Continuous

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=__**Question 15**__=

math \lim_{x\rightarrow 3} \frac{1}{x^2-9} math

a.1/9 b. math \sqrt{\frac{28}{3}} math c.-1/9 d. DNE

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 * __ Question 16 __**

math Find: \lim_{x\rightarrow 0}\tfrac{\sqrt{x^{2}+9}-3}{x^{2}} math

a. DNE b. 1/3 c. 1/6 d. 1/12 e. none of the above

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 * __ Question 17 __**

math Find: \lim_{x\rightarrow 0}\tfrac{\sqrt{2-x}-\sqrt{2}}{x} math

a. DNE b. math \frac{-\sqrt{2}}{2} math c. math \frac{-1}{\sqrt{2}} math d. math \frac{-\sqrt{2}}{4} math e. none of the above

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 * __ Question 18 __**

math Find: \lim_{x\rightarrow 0}\left | x \right | math

a. DNE b. 1 c. 0 d. -1 e. none of the above

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 * __ Question 19 __**

math Find: \lim_{x\rightarrow 0}\tfrac{ \left | x \right |}{x} math

a. DNE b. 1 c. 0 d. -1 e. none of the above

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 * Question 20**

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 * Question 22**

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 * Question 23**

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 * Question 24**