(a) lim x?0 (1 - cosx) / (x + x^2) (b) lim x?4 3(x - 4) / (x^2 - 16) (c) lim t?0 (?(8 + t) - 2) / t (d) lim x?0 (sinh x - x) / x^3 (e) lim x?? ln(3x) / x^2 (f) lim t?-? t^2 / e^{1-t} (g) lim x?0+ x^3 cot x (h) lim x?? (x tan(1/x)) (i) lim x?? (x - ln x) (j) lim x?0+ 3(x)^{x/2} (k) lim x?? (1 + x)^{1/x} (l) lim x?0+ (e^x + x)^{2/x}
Added by Linda L.
Close
Step 1
(a) \(\lim_{x \to 0} \frac{1 - \cos x}{x + x^2}\) (b) \(\lim_{x \to 4} \frac{3(x - 4)}{x^2 - 16}\) (c) \(\lim_{t \to 0} \frac{\sqrt[3]{8 + t} - 2}{t}\) (d) \(\lim_{x \to 0} \frac{\sinh x - x}{x^3}\) (e) \(\lim_{x \to \infty} \frac{\ln(3x)}{x^2}\) (f) \(\lim_{t Show more…
Show all steps
Your feedback will help us improve your experience
Sai Sai and 78 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Evaluate the limit if it exists. If the limit exists and is infinite, answer with either +∞ or -∞. If the limit does not exist, write DNE.
Adi S.
$1-4$ Given that $$\begin{array}{c}{\lim _{x \rightarrow a} f(x)=0 \quad \lim _{x \rightarrow a} g(x)=0 \quad \lim _{x \rightarrow a} h(x)=1} \\ {\lim _{x \rightarrow a} p(x)=\infty \quad \lim _{x \rightarrow a} q(x)=\infty}\end{array}$$ which of the following limits are indeterminate forms? For those that are not an indeterminate form, evaluate the limit where possible. $$\begin{array}{ll}{\text { (a) } \lim _{x \rightarrow a} \frac{f(x)}{g(x)}} & {\text { (b) } \lim _{x \rightarrow a} \frac{f(x)}{p(x)}} \\ {\text { (c) } \lim _{x \rightarrow a} \frac{h(x)}{p(x)}} & {\text { (d) } \lim _{x \rightarrow a} \frac{p(x)}{f(x)}} \\ {\text { (e) } \lim _{x \rightarrow a} \frac{p(x)}{q(x)}}\end{array}$$
Inverse Functions
Indeterminate Forms and l'Hopital's Rule
Assume that if $\lim _{x \rightarrow a} f(x)=L,$ then $\lim _{x \rightarrow a} \cos f(x)=\cos L .$ In each case evaluate the limit or indicate that the limit does not exist. (a) $\lim _{x \rightarrow 0} \cos \left(\frac{2 x}{1-2 x}\right)$ (b) $\lim _{x \rightarrow \pi / 2} \frac{\cos x}{x}$ (c) $\lim _{x \rightarrow 1} x^{3} \cos (1-x)$ (d) $\lim _{x \rightarrow 0} \frac{1-x^{2}}{1-\cos \left(x^{2}\right)}$
Limits
Basic Limit Laws
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD