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TIFR2011MathsA19
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The derivative of the function
$\int_{0}^{\sqrt{x}} e^{t^{2}}dt$
at $x = 1$ is $e^{1}$ .
tifrmaths2011
calculus
differentiation
asked
Dec 9, 2015
in
Calculus
by
makhdoom ghaya
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1
Answer
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No the Answer is $\frac{1}{2} e^{1}$... Apply Leibniz Rule
answered
Nov 25, 2019
by
seetal samal
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TIFR2011MathsA9
The function $f(x)$ defined by $f(x) = \begin{cases} ax+b & \text{x ≥ 1 } \\ x^{2}+3x+3& \text{x ≤ 1} \end{cases}$ is differentiable For a unique value of a and infinitely many values of $b$. For a unique value of $b$ and infinitely many values of $a$. For infinitely many values of $a$ and $b$. None of the above.
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TIFR2011MathsA5
The differential equation $\frac{dy}{dx}= y^{1/3}, y(0)=0$ has A unique solution No nontrivial solution Finite number of solutions. Infinite number of solutions.
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TIFR2011MathsA25
The function $f(x) = \begin{cases} 0 & \text{if x is rational} \\ x& \text{if x is irrational} \end{cases}$ is not continuous anywhere on the real line.
asked
Dec 9, 2015
in
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146
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tifrmaths2011
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continuity
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1
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4
TIFR2011MathsA15
If $A, B$ are closed subsets of $[0,\infty)$, then $A + B = \left\{x + y  x \in A, y \in B\right\}$ is closed in $[0,\infty)$
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Dec 9, 2015
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Calculus
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tifrmaths2011
calculus
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