Secant/Tangent Lines and Limits

Lesson 2-5 Review

Tangent Lines and Limits

Secant Line

Multiple Choice

Given  $$f\left(x\right)=x^2-2x$$  , find the slope of the secant line between x=-3 and x=9.

• $$4$$  

• $$-4$$  

• $$\frac{1}{4}$$  

• $$-1$$  

Tangent Line

Multiple Choice

If $$f\left(x\right)=x^2-3x$$ , find the slope of the tangent line at  $$x=2$$ .

• 2

• -3

• 1

• 3

Multiple Choice

If $$f\left(x\right)=x^2-3x$$ , find the equation of the tangent line at  $$x=2$$ . (Remember that  $$m_{\tan}=1$$  )

• $$y\ +\ 2=\left(x-2\right)$$  

• $$y=x-2$$  

• $$y=x$$  

• $$y-2=\left(x+2\right)$$  

Limits Graphically

Multiple Choice

Find $$\lim_{x\rightarrow0-}f\left(x\right)$$  .

• 0

• -5

• -6

• Does Not Exist

Multiple Choice

Find $$\lim_{x\rightarrow0+}f\left(x\right)$$  .

• 0

• -5

• -6

• Does Not Exist

Multiple Choice

Find $$\lim_{x\rightarrow0}f\left(x\right)$$  .

• 0

• -5

• -6

• Does Not Exist

Multiple Choice

Find  $$f\left(0\right)$$  

• 0

• -5

• -6

• Does Not Exist

Multiple Choice

Find $$\lim_{x\rightarrow5}f\left(x\right)$$  .

• 0

• -5

• -6

• Does Not Exist

Multiple Choice

$$\lim_{x\rightarrow\infty}f\left(x\right)=$$  

• $$-\infty$$  

• $$\infty$$  

• $$0$$  

• $$DNE$$  

Multiple Choice

Given the graph, find $$\lim_{x\rightarrow-\infty}f\left(x\right)$$  .

• $$+\infty$$  

• $$-\infty$$  

• 7

• -5

Multiple Choice

Given the graph, find $$\lim_{x\rightarrow\infty}f\left(x\right)$$  .

• $$+\infty$$  

• $$-\infty$$  

• 2

• 8

Limits Algebraically

To determine a limit algebraically as x approaches a specific value a...

1.  Substitute a into f(x)
2. Simplify/cancel factors, then substitute
3. Test left and right side limits (vertical asymptote)
4. Indeterminate

Limits Algebraically

To determine a limit algebraically as x approaches +/- infinity...

1.  Highest power in numerator (Top Heavy) = +/- infinity

2. Highest power the same in numerator/denominator (Balanced) = the ratio of the lead coefficients.

3. Highest power in the denominator (Bottom Heavy) = 0

Multiple Choice

• 0

• 1

• 8

• DNE

Multiple Choice

• 0

• $$\infty$$

• $$-\infty$$

• DNE

Multiple Choice

• 0

• 1/2

• $$\infty$$

• $$-\infty$$

Multiple Choice

• 0

• $$-\frac{4}{5}$$

• $$\infty$$

• $$-\infty$$

Multiple Choice

• $$0$$

• $$\frac{2}{5}$$

• $$\infty$$

• $$-\infty$$

Multiple Choice

What is the limit of h(x) as x approaches -4?

• $$16$$

• $$4$$

• $$-4$$

• $$DNE$$