4-7 L'Hospital's Rule

4-7 L'Hospital's Rule

Guided Notes

Multiple Choice

• 6/5
• -6/5
• 0
• ∞

Multiple Choice

What is the limit?

• DNE
• Infinity
• 6
• 12

Multiple Choice

• 0
• 1
• -32/3
• 32/3

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

Let

$$f$$  be the function defined by  $$f\left(x\right)=2x+3e^{-5x}$$ , and let  $$g$$  be a differentiable function with derivative given by   $$g\ '\ \left(x\right)=\frac{1}{x}+4\cos\left(\frac{5}{x}\right)$$ .  It is known that  $$\lim_{x\rightarrow\infty}\ g\left(x\right)=\infty$$ .  The value of  $$\lim_{x\rightarrow\infty}\ \frac{f\left(x\right)}{g\left(x\right)}$$  is

• 0

• $$\frac{1}{2}$$  

• 1

• nonexistent

Multiple Choice

Evaluate the limit. $$\lim_{x\rightarrow\ \frac{\pi}{2}}\ \frac{1-\sin x}{1+\cos\left(2x\right)}$$  

• $$\frac{1}{2}$$  

• 1

• 0

• $$\frac{1}{4}$$