Problem

4) \( \lim _{x \rightarrow 1} \frac{x^{4}-1}{x-1} \)

Answer

Expert–verified
Hide Steps
Answer

\( \lim_{x \rightarrow 1} \left[ (1^2+1) (1+1) \right] = \( 2(2) \) = 4

Steps

Step 1 ：\( \lim_{x \rightarrow 1} \frac{x^{4}-1}{x-1} \) = \( \lim_{x \rightarrow 1} \frac{(x^2+1)(x^2-1)}{x-1} \)

Step 2 ：\( \lim_{x \rightarrow 1} \left[ (x^2+1) \frac{x^2-1}{x-1} \right] \) = \( \lim_{x \rightarrow 1} \left[ (x^2+1) (x+1) \right] \)

Step 3 ：\( \lim_{x \rightarrow 1} \left[ (1^2+1) (1+1) \right] = \( 2(2) \) = 4

link_gpt

Popular Problems

Compute $\int_{0}^{\ln (2) / … Solve the triangle. \[ \mathr… QUESTION 2 - 1 POINT Solve th… 5. Suppose you are a computer… Answer the statistical measur… $(-\infty, 2) \cap(-6, \infty… A firm does not pay a dividen… Math 112 Section: 4. Tubercul… Find $y^{\prime}$ if $y=\ln \… 3. (3pts) Cherry trees in a c… More