If the function $f(x)$ defined by $\frac {x^{100}}{100}+\frac {x^{99}}{100}+\dots \frac {x^2}{100}+x+1$ then $f'(0)$ is equal to
- $100$
- $-1$
- $100 f'(0)$
- $1$
The Correct Option is D
Solution and Explanation
On differentiating both sides w.r.t. $x$, we get
$f'(x) =\frac{100 x^{99}}{100}+ \frac{99 x^{98}}{99}+...+\frac{2 x}{2}+1+0$
$\Rightarrow f'(x) =x^{99}+ x^{98}+\ldots+x+1$
Put $x=0$, we get
$f'(0) =0+0+\ldots+0+1$
$\Rightarrow f'(0) =1$
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
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is equal to __________.
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Questions Asked in KCET exam
Match the following:
In the following, \( [x] \) denotes the greatest integer less than or equal to \( x \).
Choose the correct answer from the options given below:- KCET - 2025
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- The function f(x) is given by:
For x < 0:
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Concepts Used:
Limits And Derivatives
Mathematically, a limit is explained as a value that a function approaches as the input, and it produces some value. Limits are essential in calculus and mathematical analysis and are used to define derivatives, integrals, and continuity.
Limits Formula:
Derivatives of a Function:
A derivative is referred to the instantaneous rate of change of a quantity with response to the other. It helps to look into the moment-by-moment nature of an amount. The derivative of a function is shown in the below-given formula.
Properties of Derivatives:
Read More: Limits and Derivatives