Mathematics · JEE

Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable Short Tricks for JEE

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Syllabus context

Part of Limit, Continuity and Differentiability in JEE Main Mathematics.

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Q1MathsUnit 7: Limit, Continuity and Differentiability

If the radius of a sphere is measured as

9 \mathrm{cm}

with an error of

0.03 \mathrm{cm}

then, find the approximate error in calculating its volume

Q2MathsUnit 7: Limit, Continuity and Differentiability

If the ratio of base radius and height of a cone is 1: 2 and percentage error in radius is

\lambda \%,

then the error in its volume is

Q3MathsUnit 7: Limit, Continuity and Differentiability

Function

\boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}+\mathbf{2}) \boldsymbol{e}^{-\boldsymbol{x}}

Q4MathsUnit 7: Limit, Continuity and Differentiability

The two curves

x^{3}-3 x y^{2}+2=0

and

\mathbf{3} \boldsymbol{x}^{2} \boldsymbol{y}-\boldsymbol{y}^{3}-\boldsymbol{2}=\mathbf{0}

Q5MathsUnit 7: Limit, Continuity and Differentiability

Equation of normal drawn to the graph of the function defined as

f(x)=\frac{\sin x^{2}}{x}

\boldsymbol{x} \neq \mathbf{0}

and

\boldsymbol{f}(\mathbf{0})=\mathbf{0}

at the origin is?

Q6MathsUnit 7: Limit, Continuity and Differentiability

The point on the curve

y=x^{2}

which is nearest to (3,0) is

Q7MathsUnit 7: Limit, Continuity and Differentiability

For

\boldsymbol{x} \in \boldsymbol{R}

let

\boldsymbol{f}(\boldsymbol{x})=|\sin \boldsymbol{x}|

and

g(x)=\int_{0}^{x} f(t) d t .

Let

p(x)=g(x)-\frac{2}{\pi} x

Then

Q8MathsUnit 7: Limit, Continuity and Differentiability

The normals to the curve

y=x^{2}-x+

1, drawn at the points with the abscissa

\boldsymbol{x}_{1}=\mathbf{0}, \boldsymbol{x}_{2}=-\mathbf{1}

and

\boldsymbol{x}_{3}=\frac{\mathbf{5}}{\mathbf{2}}

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