Question:
Let f: R→R such that f(1) =3 and f'(1) = 6. Then \(\lim\limits_{x\rightarrow0}\left(\frac{f(1+x)}{f(1)}\right)^{1/x}\)equals
Let f: R→R such that f(1) =3 and f'(1) = 6. Then \(\lim\limits_{x\rightarrow0}\left(\frac{f(1+x)}{f(1)}\right)^{1/x}\)equals
Updated On: Mar 12, 2025
- e1/2
- e2
- e3
- 1
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The correct answer is(B): e2
Was this answer helpful?
0
0
Top Questions on Relations and functions
- Consider a set \( S = \{a, b, c, d\} \). Then the number of reflexive as well as symmetric relations from \( S \to S \) is:
- JEE Main - 2026
- Mathematics
- Relations and functions
- Let \( A = \{-2,-1,0,1,2,3,4\} \) and \( R \) be a relation such that \[ R=\{(x,y): 2x+y \le -2,\ x\in A,\ y\in A\}. \] Let
\( l \) = number of elements in \( R \),
\( m \) = minimum number of elements to be added to \( R \) to make it reflexive,
\( n \) = minimum number of elements to be added to \( R \) to make it symmetric. Then \( (l+m+n) \) is:- JEE Main - 2026
- Mathematics
- Relations and functions
Let \(M = \{1, 2, 3, ....., 16\}\), if a relation R defined on set M such that R = \((x, y) : 4y = 5x – 3, x, y (\in) M\). How many elements should be added to R to make it symmetric.
- JEE Main - 2026
- Mathematics
- Relations and functions
- If set $A$ has 3 elements and set $B$ has 4 elements, then the number of injective mappings from $A$ to $B$ is
- IPU CET - 2025
- Mathematics
- Relations and functions
- Let A = \{1, 2, 3\}. Then, the number of relations containing (1, 2) and (1, 3), which are reflexive and symmetric but not transitive, is
- CUET (UG) - 2025
- Mathematics
- Relations and functions
View More Questions
Questions Asked in CUET PG exam
- Door is related to bang in the same way as chain is related to
- CUET (PG) - 2025
- Analogies
Find the next two terms of the series:
The given series is: \( A, C, F, J, ? \).(A) O
(B) U
(C) R
(D) V
Choose the correct answer from the options given below:
- CUET (PG) - 2025
- Letter Series
- HPV is responsible mainly for:
- CUET (PG) - 2025
- Microbiology
- Lakulish sect is related to:
- CUET (PG) - 2025
- Ancient History
- One term in the given number series is wrong. Find out the wrong term.
- CUET (PG) - 2025
- Number Series
View More Questions