2/23 Calculus - Mixed Practice #1

The answer to a limit is always the __________ of a function at the given x-value.

• intended y-value

• actual y-value

• x-value

• 0
• 1
• 2
• DNE

Find $\lim_{x\rightarrow4}\frac{x^2+3x-28}{x-4}$ . 

• 11

• 0

• DNE

• 3

• Does not exist
• -7/5
• -5/9
• -1/2

• A
• B
• C
• D

• A
• B
• D
• E

Find the slope of the tangent line to the curve

 $xy^3-x^3y=6$  at the point  $\left(1,\ 2\right)$  .

•  $-\frac{2}{5}$  

•  $-\frac{14}{11}$  

•  $-\frac{2}{11}$  

•  $\frac{4}{5}$  

If  $y=e^{-2x^3}$  , then  $\frac{\text{d}y}{\text{d}x}=$  

•  $-2x^3e^{-2x^3}$  

•  $e^{-2x^3}$  

•  $-6x^2e^{-2x^3}$  

•  $e^{-6x^2}$  

•  $-6x^2e^{-6x^2}$  

Find the derivative of y = 2x² (3x - 4)

• 6x³ - 8x²
• 18x² - 16x
• 15x² - 6x
• 6x - 4

Find the derivative of the given equation
f(x) = x⁴ + 4x³ - 2x²

• x³ + x² - x
• 4x³ + 12x² + 4x
• 4x + 12x - 4x
• 4x³ + 12x² - 4x