Question:
If h(x)=4x3-5x+7 is the derivative of f(x), then \(\lim\limits_{t\rightarrow0}\frac{f(1+t)-f(1)}{t}\) is equal to
If h(x)=4x3-5x+7 is the derivative of f(x), then \(\lim\limits_{t\rightarrow0}\frac{f(1+t)-f(1)}{t}\) is equal to
Updated On: Apr 4, 2025
- 5
- 6
- 7
- 8
- 0
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
We are given that \( h(x) = 4x^3 - 5x + 7 \) is the derivative of \( f(x) \), and we need to find the value of:
\( \lim\limits_{t \rightarrow 0} \frac{f(1+t) - f(1)}{t} \).
From the definition of the derivative, we know that:
\( \lim\limits_{t \rightarrow 0} \frac{f(1+t) - f(1)}{t} = f'(1) \).
We are given that \( h(x) = f'(x) \), so:
\( f'(1) = h(1) \).
Now, substitute \( x = 1 \) into the expression for \( h(x) \):
\( h(1) = 4(1)^3 - 5(1) + 7 \).
\( h(1) = 4 - 5 + 7 = 6 \).
The correct answer is 6.
Was this answer helpful?
0
0
Top KEAM Mathematics Questions
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
- The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is
- The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is
- Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals
- Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?
View More Questions
Top KEAM limits and derivatives Questions
- If $ f(x)=(x-2)(x-4)(x-6)....(x-2n), $ then $ f'(2) $ is
- \(\lim\limits_{t\rightarrow0}\frac{x}{\sqrt{9-x}-3}\) is equal to
- \(\lim\limits_{t\rightarrow-3}\frac{x^2+16x+39}{2x^2+7x+3}\) is equal to
- \(\lim\limits_{t\rightarrow0}\frac{tan^2(\frac{\pi}{3}+t)-3}{t}\) is equal to
- Let f(x)=√x+5 for 1≤x≤9. Then the value of c whose existence is guaranteed by the Mean Value Theorem is
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions