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
- 5
- 6
- 7
- 8
- 0
The Correct Option is B
Solution and Explanation
Top Questions on limits and derivatives
Let $\left\lfloor t \right\rfloor$ be the greatest integer less than or equal to $t$. Then the least value of $p \in \mathbb{N}$ for which
\[ \lim_{x \to 0^+} \left( x \left\lfloor \frac{1}{x} \right\rfloor + \left\lfloor \frac{2}{x} \right\rfloor + \dots + \left\lfloor \frac{p}{x} \right\rfloor \right) - x^2 \left( \left\lfloor \frac{1}{x^2} \right\rfloor + \left\lfloor \frac{2}{x^2} \right\rfloor + \dots + \left\lfloor \frac{9^2}{x^2} \right\rfloor \right) \geq 1 \]
is equal to __________.
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- Let \( f \) be the function defined by:
\[ f(x) = \begin{cases} \frac{x^2 - 1}{x^2 - 2|x-1| - 1}, & \text{if } x \neq 1, \\ \frac{1}{2}, & \text{if } x = 1. \end{cases} \] The function is continuous at:- BITSAT - 2024
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- Let \( f(x) = x^2 \log(\cos x) \log(1 + x) \) for \( x \neq 0 \), and \( f(0) = 0 \). Determine the behavior of \( f(x) \) at \( x = 0 \).
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- If \( f(x) \) is defined as follows:
\[ f(x) = \begin{cases} 4, & {if } -\infty < x < -\sqrt{5}, \\ x^2 - 1, & {if } -\sqrt{5} \leq x \leq \sqrt{5}, \\ 4, & {if } \sqrt{5} \leq x < \infty. \end{cases} \] If \( k \) is the number of points where \( f(x) \) is not differentiable, then \( k - 2 = \)- BITSAT - 2024
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Questions Asked in KEAM exam
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For the reaction:
\[ 2A + B \rightarrow 2C + D \]
The following kinetic data were obtained for three different experiments performed at the same temperature:
\[ \begin{array}{|c|c|c|c|} \hline \text{Experiment} & [A]_0 \, (\text{M}) & [B]_0 \, (\text{M}) & \text{Initial rate} \, (\text{M/s}) \\ \hline I & 0.10 & 0.10 & 0.10 \\ II & 0.20 & 0.10 & 0.40 \\ III & 0.20 & 0.20 & 0.40 \\ \hline \end{array} \]
The total order and order in [B] for the reaction are respectively:
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