Evaluate the following limit: _ x 2 x^4-16 x -2 - Vidyadip

Question

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow2}\frac{\text{x}^4-16}{{\text{x}}-2}$

✓

Answer

$\lim\limits_{\text{x}\rightarrow2}\frac{\text{x}^4-16}{{\text{x}}-2}$ $=\lim\limits_{\text{x}\rightarrow2}\frac{\big(\text{x}^2+4\big)\big(\text{x}^2+4\big)}{({\text{x}}-2)}$ $=\lim\limits_{\text{x}\rightarrow2}\frac{(\text{x}-2)(\text{x}+2)\big(\text{x}^2+4\big)}{({\text{x}}-2)}$ $=\lim\limits_{\text{x}\rightarrow2}{(\text{x}+2)\big(\text{x}^2+4\big)}$ $=(2+2)(4+4)$ $=4(8)$ $=32$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 2 marks)" from Limits→Limits — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the derivative of the function $5 \sin x-6 \cos x+7$

Convert the complex number in the polar form: $-3$

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{1-\cos2\text{x}}{3\tan^2\text{x}}$

Evaluate $\mathop {\lim }\limits_{x \to \pi } \frac{{\sin (\pi - x)}}{{\pi (\pi - x)}}$

If f, g, h are three function defined from R to R as follows: $h(x) = x^2 + 1$

For what values of a and b the intercepts cut off on the coordinate axes by the line ax + by + 8 = 0 are equal in length but opposite in signs to those cut off by the line 2x - 3y + 6 = 0 on the axes.

Evaluate $\mathop {\lim }\limits_{x \to 0} \frac{{\sin ax + bx}}{{ax + \sin bx}};$ a, b, a + b $\neq$ 0.

Find an approximation of $(0.99)^5$ using the first three terms of its expansion.

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{\text{log(2+x)}+\text{log0.5}}{\text{x}}$

Solve the inequality: $7 \leq \frac{(3 x+11)}{2} \leq 11$