related rates

related rates/implicit

Review

Multiple Choice

• 0
• 1
• -32/3
• 32/3

Multiple Choice

• 5/3
• 0
• DNE
• 1

Multiple Choice

• -1
• 1
• 0
• 12

Multiple Choice

• 0
• 5/3
• e^5x
• DNE

Multiple Choice

Evaluate the limit.
$$\lim_{x\rightarrow2}\ \frac{x^2-4x+4}{x^3-12x+16}$$  

• $$\frac{1}{4}$$  

• 4

• $$\frac{1}{6}$$  

• 6

Multiple Choice

Find the limit

• 1/4
• -1/4
• 1/16
• -1/16

Fill in the Blanks

Rachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec. How fast is the ladder sliding down the wall when the tip of the ladder is 5 ft high?

Multiple Choice

Find dy/dx

xy+y²=2

• -y/(x+2y)

• y/(x+2y)

• -3y/x

• -3x/y

Multiple Choice

Brandon is starting to clean up after a birthday party. He begins deflating each spherical balloon by puncturing a hole in each. The air leaves the balloon at a constant rate of 2 cm³/sec. How long is the diameter when the diameter is changing at a rate of 3 cm/sec?

• .424 cm

• .651 cm

• 1.333 cm

• 1.155 cm

Multiple Choice

Find dy/dx at the given point

x³ +2xy -y²=11 at (2,3)

• -4/7

• 12

• -9

• 9

Multiple Select

Find the  $$\frac{dy}{dx}$$  for $$x^3+y^3=3xy^2$$  by using Implicit Differentiation

• $$\frac{2y^2-x^2}{2y-2xy}$$  

• $$\frac{y^2-x^2}{y^2-2xy}$$  

• $$\frac{y^2+x^2}{2y-2xy}$$  

Open Ended

Find

$$\frac{d^2y}{dx^2}$$   given  $$x^2+y^2=100$$  

Fill in the Blanks

Solve the following question. Round to three decimals.

Fill in the Blanks

Solve and round to three decimals.