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India
Class XI

Applications of Limits

Interactive practice questions

Find the asymptotes of $f\left(x\right)=\frac{e^x}{e^3-e^x}$f(x)=exe3ex.

Write the equations of all asymptotes on the same line, separated by commas.

Easy
< 1min

A particle with a rest mass $m_0$m0 and a velocity $v$v has a mass $m=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}$m=m01v2c2, where $c$c is the speed of light.

What value does the mass approach as the velocity approaches the speed of light?

Easy
< 1min

The total mass (in kilograms) of fish in a particular lake after $t$t years is modelled by $B\left(t\right)=\frac{4\times10^7}{1+6e^{-\frac{3t}{8}}}$B(t)=4×1071+6e3t8.

What will the total mass approach in the long run?

Easy
< 1min

As each day passes, the water in a swimming pool is getting dirtier and dirtier. The concentration of dirt in the pool (in grams per litre) after $t$t days is modelled by $C\left(t\right)=\frac{4t}{90+t}$C(t)=4t90+t.

What is the concentration of dirt in the pool in the long run (as $t$t approaches infinity)?

Easy
2min
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Outcomes

11.C.LD.1

Derivative introduced as rate of change both as that of distance function and geometrically, intuitive idea of limit. Definition of derivative, relate it to slope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

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