Home
Class 12
MATHS
Let f be differentiable function such t...

Let f be differentiable function such that
`f'(x)=7-3/4(f(x))/x,(xgt0) and f(1)ne4" Then " underset(xto0^+)limxf(1/x)`

A

exists and equals `4//7`

B

exists and equals 0

C

exist and equals 4

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
C
Let `f(x)=y`
`(dy)/(dx)=7-(3)/(4)(y)/(x)(x gt 0)`
`(dy)/(dx)+(3)/(4)(y)/(x)=7`
If `e^(int(3)/(4x))=x^(3//4)`
`yx^(3//4)=7 int x^(3//4) dx+c`
`yx^(3//4)=4x^(7//4)+c`
`y=4x+cx^(-3//4)`
`f((1)/(x))=(4)/(x)+cx^(3//4)` `xf((1)/(x))=4+cx^(7//4)`
`lim_(x to 0^(+)) xf ((1)/(x))=4`
Promotional Banner

Topper's Solved these Questions

  • JEE MAIN REVISION TEST-3 (2020)

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

  • JEE Main Revision Test-20 | JEE-2020

    VMC MODULES ENGLISH|Exercise MATHEMATICS|25 Videos

  • JEE Main Revision Test-6 | JEE-2020

    VMC MODULES ENGLISH|Exercise MATHEMATICS|25 Videos

Similar Questions

Explore conceptually related problems

Let f be differentiable function such that f'(x)=7-3/4(f(x))/x,(xgt0) and f(1)ne4" Then " lim_(xto0^+) xf(1/x)

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then f(x) is

Let f be a differentiable function such that f'(x) = f(x) + int_(0)^(2) f(x) dx and f(0) = (4-e^(2))/(3) . Find f(x) .

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1 +x) then (1) g(x) is an odd function (2) g(x) is an even function (3) graph of f(x) is symmetrical about the line x= 1 (4) f'(1)=0

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1 +x) then (1) g(x) is an odd function (2) g(x) is an even function (3) graph of f(x) is symmetrical about the line x= 1 (4) f'(1)=0

Let f : R to R be a differentiable function satisfying f'(3) + f'(2) = 0 , Then underset(x to 0) lim ((1+f(3+x)-f(3))/(1+f(2-x)-f(2)))^(1/x) is equal to

If f:RR-> RR is a differentiable function such that f(x) > 2f(x) for all x in RR and f(0)=1, then

Let f(x) be a function such that f'(a) ne 0 . Then , at x=a, f(x)

Let f be a differentiable function satisfying f(xy)=f(x).f(y).AA x gt 0, y gt 0 and f(1+x)=1+x{1+g(x)} , where lim_(x to 0)g(x)=0 then int (f(x))/(f'(x))dx is equal to