COMEDK · Maths · 16. Limits
The value of \(\lim _\limits{x \rightarrow 0} \dfrac{e^{a x}-e^{b x}}{2 x}\) is equal to
- A 0
- B \(\dfrac{e^{a b}}{2}\)
- C \(\dfrac{a+b}{2}\)
- D \(\dfrac{a-b}{2}\)
Answer & Solution
Correct Answer
(D) \(\dfrac{a-b}{2}\)
Step-by-step Solution
Detailed explanation
The limit is given by \(L = \lim_{x \rightarrow 0} \dfrac{e^{ax} - e^{bx}}{2x}\). Since the limit is of the form \(\dfrac{0}{0}\) as \(x \rightarrow 0\), L'Hopital's rule can be applied by differentiating the numerator and the denominator with respect to \(x\).…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- \(\int_{\dfrac{\pi}{6}}^{\dfrac{\pi}{3}} \dfrac{1}{1+\sqrt{\tan x}} d x=\)COMEDK 2025 Medium
- The total number of terms in \((x-y)^{20}+(x+y)^{20}\) isCOMEDK 2024 Easy
- If for \(\mathrm{a}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+\hat{\mathrm{k}}, \mathrm{b}=\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}\) and \(\mathrm{c}=-3 \hat{\mathrm{i}}+\hat{\mathrm{j}}+2 \hat{\mathrm{k}}\), then find [a b c \(]\).COMEDK 2021 Easy
- If \(2 A+3 B=\left[\begin{array}{ccc}2 & -1 & 4 \\ 3 & 2 & 5\end{array}\right]\) and \(A+2 B=\left[\begin{array}{lll}5 & 0 & 3 \\ 1 & 6 & 2\end{array}\right]\) then \(B=\)COMEDK 2023 Easy
- If \(A, B\) and \(C\) are mutually exclusive and exhaustive events of a random experiment such that \(P(B)=\dfrac{3}{2} P(A)\) and \(P(C)=\dfrac{1}{2} P(B)\), then \(P(A \cup C)\) equals toCOMEDK 2023 Easy
- \(\int\left(e^{x \log _e 6}\right) e^x d x=\phi(x)+c\) then \(\phi(x)=\)COMEDK 2025 Easy
More PYQs from COMEDK
- The maximum number of electrons which can be held by subshell with azimuthal quantum number \(' l\) in an atom is given byCOMEDK 2024 Medium
- Assuming, \(R=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\) and \(\gamma=1.4\) the values of \(C_{p}\) and \(C_{V}\) of a gas areCOMEDK 2012 Easy
- The magnitude of \(I\) in ampere unit is
COMEDK 2017 Medium - \(\cos ^{2} \frac{\pi}{12}+\cos ^{2} \frac{\pi}{4}+\cos ^{2} \frac{5 \pi}{12}=\)COMEDK 2018 Easy
- Two statements, One Assertion [A ] and the other Reason [ R ] are given. Identify the correct option Assertion [A]: The decreasing order of the acidic character of the following is \(\mathrm{B}>\mathrm{D}>\mathrm{A}>\mathrm{C}\)
Reason \([\mathrm{R}]\) : Fluorine has larger -I effect than Cl and Br .COMEDK 2025 Medium - The volume of \(\mathrm{H}_{2}\) obtained at \(\mathrm{STP}\), when \(\mathrm{Mg}\) obtained by passing a current of \(0.5 \mathrm{~A}\) through molten \(\mathrm{MgCl}_{2}\) for \(32.2\) min is treated with excess of dilute HCl is approximately
[Equivalent mass of \(\mathrm{Mg}=12\) ]COMEDK 2012 Hard