enEnglishguગુજરાતી
JEE Mains · Maths · STD 11 - 12. limits
Let \(f(x)\) be a differentiable function at \(x=a\) with \(f^{\prime}(a)=2\) and \(f(a)=4\). Then \(\lim _{x \rightarrow a} \frac{x f(a)-a f(x)}{x-a}\) equals ...... .
- A \(2 a +4\)
- B \(4-2 a\)
- C \(2 a-4\)
- D \(a +4\)
Answer & Solution
Correct Answer
(B) \(4-2 a\)
Step-by-step Solution
Detailed explanation
\(f^{\prime}(a)=2, f(a)=4\) \(\lim _{x \rightarrow a} \frac{x f(a)-a f(x)}{x-a}\) \(\Rightarrow \lim _{x \rightarrow a} \frac{f(a)-a f^{\prime}(x)}{1} \quad\) (Lopitals rule) \(=f(a)-a f^{\prime}(a)\) \(=4-2 a\)
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
- The sum of all the local minimum values of the twice differentiable function \(\mathrm{F}: \mathrm{R} \rightarrow \mathrm{R}\) defined by \(f(x)=x^{3}-3 x^{2}-\frac{3 f^{\prime \prime}(2)}{2} x+f^{\prime \prime}(1)\) is:JEE Mains 2021 Hard
- If \(\alpha, \beta,\) where \(\alpha<\beta\), are the roots of the equation \(\lambda x^{2}-(\lambda+3)x+3=0\) such that \(\frac{1}{\alpha}-\frac{1}{\beta}=\frac{1}{3},\) then the sum of all possible values of \(\lambda\) is:JEE Mains 2026 Medium
- If \(\sum_{k=1}^{10} \frac{k}{k^{4}+k^{2}+1}=\frac{m}{n}\), where \(m\) and \(n\) are coprime, then \(m+n\) is equal to.JEE Mains 2022 Hard
- If the four distinct points \((4,6),(-1,5),(0,0)\) and \((\mathrm{k}, 3 \mathrm{k})\) lie on a circle of radius r , then \(10 \mathrm{k}+\mathrm{r}^2\) is equal toJEE Mains 2025 Medium
- Let \(y = y\left( x \right)\) be the solutions of the differential equation, \(\left( {{x^2} + 1} \right)^2\,\frac{{dy}}{{dx}} + 2x\left( {{x^2} + 1} \right)\,y = 1\) such that \(y\left( 0 \right) = 0\). If \(\sqrt a y\left( 1 \right) = \frac{\pi }{{32}}\), then the value of \(‘a’\) isJEE Mains 2019 Hard
- Let the mean and variance of \(8\) numbers \(x , y , 10\), \(12,6,12,4,8\), be \(9\) and \(9.25\) respectively. If \(x > y\), then \(3 x-2 y\) is equal to \(...........\).JEE Mains 2023 Hard
More PYQs from JEE Mains
- Two cards are drawn successively with replacement from a well shuffled deck of \(52\) cards. Let \(X\) denote the random variable of number of aces obtained in the two drawn cards. Then \(P\,\left( {X = 1} \right)\, + P\,\left( {X = 2} \right)\) equalsJEE Mains 2019 Hard
- The number of rational terms in the binomial expansion of \(\left(4^{\frac{1}{4}}+5^{\frac{1}{6}}\right)^{120}\) is \(....\)JEE Mains 2021 Medium
- If the system of linear equations \(2 \mathrm{x}+2 \mathrm{ay}+\mathrm{az}=0\) ; \(2 x+3 b y+b z=0\) ; \(2 \mathrm{x}+4 \mathrm{cy}+\mathrm{cz}=0\) ; where \(a, b, c \in R\) are non-zero and distinct; has a non-zero solution, thenJEE Mains 2020 Hard
- A light ray emerging from the point source placed at \(P( 1, 3)\) is reflected at a point \(Q\) in the axis of \(x\). If the reflected ray passes through the point \(R\) (\(6, 7)\), then the abscissa of \(Q\) isJEE Mains 2013 Hard
- Let \([\bullet]\) be the greatest integer function. If \( \alpha=\int_{0}^{64}(x^{1/3}-[x^{1/3}])dx, \) then \( \frac{1}{\pi}\int_{0}^{\alpha\pi}(\frac{sin^{2}\theta}{sin^{6}\theta+cos^{6}\theta})d\theta \) is equal to ___ .JEE Mains 2026 Medium
- Let \(f: R \rightarrow R\) satisfy \(f(x+y)=2^{x} f(y)+4^{y} f(x), \forall x\), \(y \in R\). If \(f(2)=3\), then \(14 \cdot \frac{f^{\prime}(4)}{f^{\prime}(2)}\) is equal toJEE Mains 2022 Hard