Question: The value of α so that $\lim _ { x \rightarrow 0 }$ $\frac{1}{x^{2}}$ (e<sup>αx</sup> – e<sup>x<...

Question

The value of α so that $\lim _ { x \rightarrow 0 }$ $\frac{1}{x^{2}}$ (e^αx – e^x – x ) = $\frac{3}{2}$ is

Answer 1

Using L′ Hospital $\operatorname { Lim } _ { x \rightarrow 0 }$

Nr → 0 for x → 0

⇒ αe⁰ – e⁰ – 1 = 0 or α = 2

Question: The value of α so that \(\lim _ { x \rightarrow 0 }\) \(\frac{1}{x^{2}}\) (e<sup>αx</sup> – e<sup>x<...