Evaluate the following limit: _ x 0 e^x-1 1- - Vidyadip

Question

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^\text{x}-1}{\sqrt{1-\cos\text{x}}}$

✓

Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^\text{x}-1}{\sqrt{1-\cos\text{x}}}$ $=\lim\limits_{\text{x}\rightarrow0}\frac{\big(\text{e}^\text{x}-1\big)\big(\sqrt{1+\cos\text{x}}\big)}{\big(\sqrt{1-\cos\text{x}}\big)\big(\sqrt{1+\cos\text{x}}\big)}$ $=\lim\limits_{\text{x}\rightarrow0}\frac{\big(\text{e}^\text{x}-1\big)\big(\sqrt{1+\cos\text{x}}\big)}{\sin\text{x}}$ Both numerator and denominator are both zeros for x = 0 hence limit can not exist.

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 distance between the parallel lines 3x – 4y + 7 = 0 and 3x – 4y + 5 = 0

Solve $x^2 + 3x + 9 = 0$

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow{\infty}}\frac{(3\text{x}-1)(4\text{x}-2)}{(\text{x}+8)(\text{x}-1)}$

Show the following quadratic equation: $x^2 - (2 + i) x - (1 - 7i) = 0$

Find the derivative of $\frac{{{x^n} - {a^n}}}{{x - a}}$ for some constant a.

Find the coordinates of the point which divides the line segment joining the points (-2, 3, 5) and (1, -4, 6) in the ratio 2 : 3 internally.

Prove that: $\tan\frac{\pi}{12}+\tan\frac{\pi}{6}+\tan\frac{\pi}{12}\tan\frac{\pi}{6}=1$

Show the of the following progression is G.P. Also, find the common ratio in case:$\text{a}\frac{3\text{a}^2}{4},\frac{9\text{a}^3}{16},\cdots$

If $\left(\frac{1+i}{1-i}\right)^{m} = 1$ then find the least positive integral value of m.

Find the equation of the line whose perpendicular distance from the origin is 4 units and the angle which the normal makes with positive direction of x-axis is 15°.