﻿ Let f : 0, ∞ → 0, ∞ be a differentiable function such that f(1) = e and limt→x t2f2x - x2f2tt - x. If f(x) = 1, then x is equal to | Limits and Derivatives

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# Limits and Derivatives

#### Multiple Choice Questions

111.

• $\frac{1}{\mathrm{k}}$

• $\frac{2}{\mathrm{k}}$

112.

• $\frac{1}{2}$

• 1

• 2

113.

• ${\mathrm{tan}}^{-1}\left(\frac{5}{\sqrt{3}}\right)$

• ${\mathrm{tan}}^{-1}\left(\sqrt{\frac{5}{3}}\right)$

• ${\mathrm{tan}}^{-1}\left(\frac{2}{\sqrt{3}}\right)$

• $\frac{\mathrm{\pi }}{3}$

114.

115.

• 2

• 1

• e

• e2

116.

117.

#### Multiple Choice Questions

118.

• $\left(\frac{2}{9}\right){\left(\frac{2}{3}\right)}^{1}{3}}$

• ${\left(\frac{2}{3}\right)}^{4}{3}}$

• ${\left(\frac{2}{9}\right)}^{4}{3}}$

• $\left(\frac{2}{3}\right){\left(\frac{2}{9}\right)}^{1}{3}}$

# 119.$\frac{1}{\mathrm{e}}$ 2e $\frac{1}{2\mathrm{e}}$ e

A.

$\frac{1}{\mathrm{e}}$

• is equal to $\sqrt{\mathrm{e}}$