Differential Calculus> let f(x)=min{1-tan^n x,1-sin^n x,1-x^n } ...

let f(x)=min{1-tan^n x,1-sin^n x,1-x^n } xbelongs to(-pi/2,pi/2) where n belong to N.Then the left hand derivative of the f(x)atx=pi/4 is :A.-2nb.-2n+1c.-n(pi/4)^n-1D.n(pi/4)^ n-1

rajat , 10 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:

$f(x) = min(1-sin^{n}x ,1 -x^{n},1-tan^{n}x)$

$sinx < x < tanx$

$sin^{n}x < x^{n} < tan^{n}x$

$-sin^{n}x > -x^{n} > -tan^{n}x$

$1-sin^{n}x >1 -x^{n} > 1-tan^{n}x$

$LHD = \lim_{h\rightarrow 0}\frac{((1-tan^{n}(\frac{\pi }{4}-h))-(1-1))}{-h}$

$LHD = \lim_{h\rightarrow 0}\frac{(1-tan^{n}(\frac{\pi }{4}-h)}{-h}$

It is zero by zero indeterminent form. Apply L’Hospital Rule,

$LHD = \lim_{h\rightarrow 0}\frac{(ntan^{n-1}(\frac{\pi }{4}-h).sec^{2}(\frac{\pi }{4}-h)}{-1} = -2n$

Thanks & Regards

Jitender Singh

IIT Delhi

askIITians Faculty

Provide a better Answer & Earn Cool Goodies

Enter text here...

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

Ask a Doubt

Get your questions answered by the expert for free

Enter text here...

the diameter of a roller is 84 cm and its length is 120 cm. it takes 500 complete revolution tomove once over to level a playground. find the area of the playground in square m?

Differential Calculus

1 Answer Available

Last Activity: 2 Year ago(s)

Find dy/DX when y=x^sinx+sin-1√x. Please give me the solution of this problem.

Differential Calculus

0 Answer Available

Last Activity: 2 Year ago(s)

If domain of f(x) is [-1, 2], then find the domain of f([x]-x^2+4), where [ ]denotes greatest integer function.

Differential Calculus

0 Answer Available

Last Activity: 2 Year ago(s)

Solve the differential equation y’’+2ty’-4y=1, y(0)=y’(0)=0.

Differential Calculus

0 Answer Available

Last Activity: 2 Year ago(s)

Example 20. (i) In a AABC, find the maxima and minima of u = sin A sin B sin Cwhere A + B + C = T(ii) In a plane triangle ABC, find the maximum value of cosA cosB cosC.

Differential Calculus

0 Answer Available

Last Activity: 2 Year ago(s)

View all Questions

Differential Calculus> let f(x)=min{1-tan^n x,1-sin^n x,1-x^n } ...

let f(x)=min{1-tan^n x,1-sin^n x,1-x^n } xbelongs to(-pi/2,pi/2) where n belong to N.Then the left hand derivative of the f(x)atx=pi/4 is :A.-2nb.-2n+1c.-n(pi/4)^n-1D.n(pi/4)^ n-1

rajat , 10 Years ago

Jitender Singh

Provide a better Answer & Earn Cool Goodies

LIVE ONLINE CLASSES

Ask a Doubt

Other Related Questions on Differential Calculus

the diameter of a roller is 84 cm and its length is 120 cm. it takes 500 complete revolution tomove once over to level a playground. find the area of the playground in square m?

Differential Calculus

Find dy/DX when y=x^sinx+sin-1√x. Please give me the solution of this problem.

Differential Calculus

If domain of f(x) is [-1, 2], then find the domain of f([x]-x^2+4), where [ ]denotes greatest integer function.

Differential Calculus

Solve the differential equation y’’+2ty’-4y=1, y(0)=y’(0)=0.

Differential Calculus

Example 20. (i) In a AABC, find the maxima and minima of u = sin A sin B sin Cwhere A + B + C = T(ii) In a plane triangle ABC, find the maximum value of cosA cosB cosC.

Differential Calculus