NIMCET Differentibility Previous Year Question Paper and Solution with PDF

NIMCET Previous Year Questions (PYQs) – Differentibility

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Previous Year Questions

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Previous Year Questions
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Qus : 1

Video Solution Discussion

Qus : 2

Let

f (x) = {\begin{cases} x^{2} \sin \frac{1}{x} & , x \neq 0 \\ 0 & , x = 0 \end{cases}

Then which of the follwoing is true

Video Solution Discussion

Qus : 3

Let

f : R \to R

be a function such that

f (0) = \frac{1}{π}

and

f (x) = \frac{x}{e^{π x} - 1}

for

x \neq 0

, then

Video Solution Discussion

Qus : 4

The set of points, where

is differential in

Video Solution Discussion

Qus : 5

Let

R \to R

be any function defined as

f (x) = {\begin{cases} x^{α} \sin \frac{1}{x^{β}} & , x \neq 0 \\ 0 & , x = 0 \end{cases}

α, β \in R

. Which of the following is true? (

R

denotes the set of all real numbers)

Video Solution Discussion

Qus : 6

The slope of the function

f (x) = {\begin{cases} x^{2} \sin (\frac{1}{x}), & if x \neq 0, \\ 0, & if x = 0 \end{cases}

Video Solution Discussion

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NIMCET Previous Year Questions (PYQs) – Differentibility

Solution

Solution

Solution

Analysis of Continuity and Differentiability

✅ Continuity at $x = 0$ :

✏️ Differentiability at $x = 0$ :

✅ Final Result:

Solution

Solution

Solution

NIMCET

NIMCET

NIMCET Previous Year Questions (PYQs) – Differentibility

✓Solution

✓Solution

✓Solution

Analysis of Continuity and Differentiability

✅ Continuity at x=0:

✏️ Differentiability at x=0:

✅ Final Result:

✓Solution

✓Solution

✓Solution

NIMCET

NIMCET

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Solution

Solution

Solution

✅ Continuity at $x = 0$ :

✏️ Differentiability at $x = 0$ :

Solution

Solution

Solution