Home
Class 12
MATHS
f(x)=|{:(cos x, x, 1),(2sin x, x^(2), 2x...

` f(x)=|{:(cos x, x, 1),(2sin x, x^(2), 2x),(tan x, x, 1):}|." Then find the vlue of lim_(x to 0) (f'(x))/(x).`

Text Solution

Verified by Experts

`f'(x)=|{:(-sin x, 1, 0),(2 sin x, x^(2), 2x),(tan x , x, 1):}|+|{:(cos, x, 1),(2 cos x, 2x, 2),(tan x, x, 1):}|`
`|{:(cosx, x, 1),(2sin x, x^(2),2x),(sec^(2)x, 1,0):}|`
`rArr" "f'(0)=|{:(0,1,0),(0,0,0),(0,0,1):}|+|{:(1,0,1),(2,0,2),(0,0,1):}|+|{:(1,0,1),(0,0,0),(1,1,0):}|=0`
`"Now ,"underset(xrarr0)lim(f(x))/(x)=underset(xrarr0)limf'(x)(as f(0)=0)`
`f'(0)=0`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.1|7 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.2|38 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|25 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

f(x)= |{:(cos x,,x,,1),(2sin x ,,x^(2),,2x),(tanx ,, x,,1):}| then find the value of lim_(xto 0) (f(x))/(x)

f'(x) = |{:(cos x , x , 1),(2sin x,x^(2),2x),(tan x, x,1):}| . The value of underset(x rarr 0)(lim) (f(x))/(x) is equal to

Let f(x)=|(cosx,x,1),(2sinx,x^(2),2x),(tan x,x,1)| then lim_(xto0)(f(x))/(x^(2)) is given by

"Let f(x) "=|{:(cos x" " sin x" " cos x),(cos 2x" "sin 2x" "2cos 2x),(cos 3x" "sin 3x" "3cos 3x):}|" Then find the vlue of "f'(0) and f'(pi//2).

"Let f(x) "=|{:(cos x" " sin x" " cos x),(cos 2x" "sin 2x" "2cos 2x),(cos 3x" "sin 3x" "3cos 3x):}|" Then find the vlue of "f'(0) and f'(pi//2).

If f (x)= |{:(x cos x, 2x sin x, x tan x),(1,x,1),(1,2x,1):}|, find lim _(xto0) (f(x))/(x ^(2)).

let f(x)=det[[cos x,x,12sin x,x^(2),2xtan x,x,1]]. then lim_(x rarr0)(f'(x))/(x)=

Let f(x) =|{:(secx,x^(2),x),(2sinx,x^(3),2x^(2)),(tan3x,x^(2),x):}|lim_(x to 0)f(x)/(x^(4)) is equal to

If f(x) = |(sin x,cos x,tan x),(x^(3),x^(2),x),(2x,1,1)|, " then " lim_(x rarr 0) (f (x))/(x^(2)) , is