The value of limx→0 eax−ebxx, is - Infinity Learn by Sri Chaitanya

A
$a + b$
B
$a - b$
C
$e^{a b}$
D
1

Solution:

We have,

$\begin{array}{l} lim_{x \to 0} \frac{e^{a x} - e^{b x}}{x} = lim_{x \to 0} \{\frac{(e^{a x} - 1)}{x} - \frac{(e^{b x} - 1)}{x}\} \\ = a lim_{x \to b} \frac{e^{a x} - 1}{a x} - b lim_{x \to 0} \frac{e^{b x} - 1}{b x} = a \times 1 - b \times 1 = a - b \end{array}$

Related content

Test your English Vocabulary

CUET Exam Dates 2024 – Application Form, Fees, Eligibility

CBSE Class 12 IP Answer Key 2024,Informatics Practices Paper Solution For SET 1, 2, 3, 4

CUET UG Cut Off 2024, Category, Universities and Colleges Wise Expected Cut Off

Modal Verbs

Helping Verbs

Letter To Your Friend About Your School Trip

Action Verbs

CUET 2024 – List of Colleges and Participating Universities Accepting CUET Exam Score

SRMJEEE Online Test Series – Practice Papers