AP Calculus BC : 1.6 Determining Limits Using Algebraic Manipulation- Exam Style questions with Answer- MCQ

If $f(x)=\frac{\cos x-1}{\sin ^{2}x}$ ,then is equivalent to which of the following? $f (x) = \frac{\cos x - 1}{\sin^{2} x}$

Answer/Explanation

Ans:A

A 0

B $\frac{5}{3}$

C 3

D ∞

Answer/Explanation

Ans:C

If $f$ is the function defined by then is equivalent to which of the following?

Answer/Explanation

Ans:B

Find the limit:$\lim_{t\rightarrow 0}\frac{\sqrt{4-t}-2}{t}$
(A) ∞
(B) −∞
(C) − 1
(D) The limit does not exist.

Answer/Explanation

Ans:(C)

Multiply the expression by a convenient form of 1 and obtain