SATHEE: Limit Continuity and Differentiability 1 Question 10

Limit Continuity and Differentiability 1 Question 10

11. If $lim_{x \to \infty} \frac{x^{2} + x + 1}{x + 1} - a x - b = 4$ , then

(a) $a = 1, b = 4$

(b) $a = 1, b = - 4$

(d) $a = 2, b = 3$

Show Answer

Answer:

Correct Answer: 11. (b)

Solution:

Here, $lim_{x \to 0} (\sin x)^{1 / x} + lim_{x \to 0} {\frac{1}{x}}^{\sin x}$

$= 0 + lim_{x \to 0} e^{\log \frac{1}{x}} = e^{lim_{x \to 0} \frac{\log (1 / x)}{cosec x}} \begin{aligned} lim_{x \to 0} (\sin x)^{1 / x} \to 0 \\ as, (decimal)^{\infty} \to 0 \end{aligned}$

Applying L’Hospital’s rule, we get

$e^{lim_{x \to 0} \frac{x - \frac{1}{x^{2}}}{- cosec x \cot x}} = e^{lim_{x \to 0} \frac{\sin x}{x} \tan x} = e^{0} = 1$

Limit Continuity and Differentiability 1 Question 10

11. If $lim_{x \to \infty} \frac{x^{2} + x + 1}{x + 1} - a x - b = 4$ , then

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Limit Continuity and Differentiability 1 Question 10

11. If limx→∞x2+x+1x+1−ax−b=4, then

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu

11. If $lim_{x \to \infty} \frac{x^{2} + x + 1}{x + 1} - a x - b = 4$ , then