Limits and Derivatives

Find the second derivative of y=(2x+1)^2+x^3.

8+6x

6+4x

x+1

(2x+1)^3

. Evaluate the limits of lim (x^3-2x+9) /(2x^3-8).

-9/8

½

0

α

What is the first derivative dy/dx of the expression (xy)^x=e.

–y(1-ln xy)/x^2

0

–y(1+ln xy)/x

x/y

If y1=2x+4 and y2=x^2+C, find the value of C such that y2 is tangent to y1.

6

7

4

5

Find the second derivative of y=2x+3(4x+2)^3 when x=1.

1728

1541

1642

1832

Find y’ in the following equation y=4x^2-3x-1.

8x-x

8x-3

4x-3

2x-3

Find the second derivative of y=(2x+4)^2 x^3.

x^2(80x+192)

x^2(20x+60)

2x+4

x^3(2x+80)

Evaluate the lim (x^2-16)/(x-4

16

0

8

1

Find the slope of (x^2)y=8 at the point (2,2).

-1/2

-1

2

-2

Evaluate the limit (x-4)/(x^2-x-12) as x approaches 4

undefined

infinity

0

1/7

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Limits and Derivatives

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