Exam 1 Review

Domains

100

sqrt(x-4)

[4,∞)

200

3/x²-9

(−∞,−3)∪(−3,3)∪(3,∞)

300

sqrt(x-3)/x-5

[3,5)∪(5,∞)

400

sqrt(5-x)/sqrt(x-1)

(1,5]

500

sqrt(x-3)/sqrt(x+2)

[3,∞) 

STRICT CONDITION (due to the x>−2)

Limits

100

Evaluate the limit as x apporches infinity of 3/x² -3

0

200

Evaluate the limit as x approaches 3 of x²-9/x-3

6

300

Evaluate the limit as x approaches infinity of 5x²+2/2x²-7

5/2

400

Evaluate the limit as x approaches infinity of 3x³-x/x²+5

+∞

500

Evaluate the limit as x approaches infinity of 2x-sqrt(x)/x+3

2

Equation of Tangent Line

100

Find the derivative of f(x)=1/x at x=1 using the limit definition

-1

200

Use the limit definition to find f′(2) if f(x)=x²

4

300

Find f'(2) using limit as x approaches 2 of f(x)- f(2)/x-2 

if f(x)=2/x

-1/2

400

Find an equation of the tangent line to the parabola y = x² at the point (1, 1)

y-1=2(x-1)

500

Let f(x)=7/sqrt(x),

Find the slope m of the tangent line to the graph of f at the point where x = a.

-7/2a^3/2

Piecewise

100

Evaluate x as it approaches 1 FROM LEFT HAND SIDE of 

f(x)={ x+2 if x<1, 3x−1 if x≥1

3

200

Evaluate the limit as x approaches 2 FROM THE RIGHT HAND SIDE of

f(x)= {2x²−1 if x<2, x + 5 if x≥2

7

300

Evaluate the limit as x approaches 2 of

f(x)={x²−4 if x<2, 2x−4 if x≥2

0

400

Evaluate the limit as x approaches 3 of

f(x)={x²+1 if x<3, 5x−8 if x≥3

DNE

500

Fine the value of x that makes the limit as x approaches 4 exist

f(x)={ax+2 if x<4, x²−6 if x≥4

2

Derivatives

100

x⁵−4x+9

5x⁴-4

200

y=sqrt(x)+3/x

1/2x^-1/2 -3x^-2

300

y=x²+1/x

x²-1/x²

400

e^x+2+x³+e^π

e^x+2+3x²

500

y=e^x+1/x²

(e^x+1)(x²) - (e^x+1)(2x)/x⁴