AP EAMCET · Maths · Continuity and Differentiability
\[
f(x)= \begin{cases}(1+3 x)^{\frac{4}{x},} & \text { if } x \neq 0, \\ a, & \text { if } x=0 .\end{cases}
\]
If \(f\) is continuous, then \(\log a=\)
- A \(\frac{1}{3}\)
- B \(\frac{3}{4}\)
- C \(\frac{4}{3}\)
- D 12
Answer & Solution
Correct Answer
(D) 12
Step-by-step Solution
Detailed explanation
No solution. Refer to answer key.
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 area (in sq. units) of the triangle formed by the lines \(x^2-3 x y+y^2=0\) and \(x+y+1=0\), isAP EAMCET 2014 Medium
- If \(\int \frac{x^4+1}{x^2+1} d x=A x^3+B x^2+C x+D \operatorname{Tan}^{-1} x+E\), then \(A+B+C+D=\)AP EAMCET 2025 Medium
- If \(\mathrm{A}\) and \(\mathrm{B}\) are the points of intersection of the circles \(x^2+y^2-4 x+6 y-3=0\) and \(x^2+y^2+2 x-2 y-2=0\) then the distance between \(\mathrm{A}\) and \(\mathrm{B}\) isAP EAMCET 2023 Medium
- If \(y=5 x^2+6 x+6, x=2\) and \(\Delta x=0.00 \mathrm{l}\), then the values of \(\Delta y\) and \(d y\) respectively areAP EAMCET 2021 Medium
- If \(P(0,7,10), Q(-1,6,6)\) and \(R(-4,9,6)\) are three points in the space, then \(P Q R\) isAP EAMCET 2019 Easy
- A closed cylinder of given volume will have least surface area when the ratio of its height and base radius isAP EAMCET 2022 Medium
More PYQs from AP EAMCET
- The number of all 8 digit odd numbers isAP EAMCET 2023 Easy
- Consider a gas phase reaction which occurs in a closed vessel
\(2 \mathrm{~A} \rightarrow 4 \mathrm{~B}+\mathrm{C}\)
The concentration of \(\mathrm{B}\) is found to be increased by \(5 \times 10^{-3} \mathrm{~mol} \mathrm{~L}^{-1}\) in 10 seconds.
The rate of disappearance of \(\mathrm{A}\) (in \(\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}\) ) isAP EAMCET 2023 Easy - The displacement of a particle starting from rest at is given by . The time in seconds at which the particle will attain zero velocity isAP EAMCET 2021 Easy
- Ethylene on reaction with Baeyer's reagent gives the compound \(\underline{\underline{A}}\). In the preparation of co-polymer X, compound A is used as monomer. What is X?AP EAMCET 2017 Easy
- \(A(3,2,-1), B(4,1,1), C(6,2,5)\) and \(D(3,3,3)\) are four points. \(G_1, G_2, G_3\) and \(G_4\) respectively are the centroids of the triangles \(\triangle B C D, \triangle C D A\), \(\triangle D A B\) and \(\triangle A B C\). The point of concurrence of the lines \(A G_1, B G_2, C G_3\) and \(D G_4\) isAP EAMCET 2018 Easy
- The sum of the non-real roots of \(\left(p^2+p-3\right)\left(p^2+p-2\right)-12=0\) isAP EAMCET 2018 Easy