Home
Class 11
MATHS
If lim(x->0) (a+bx sin x + c cosx)/x^4=2...

If `lim_(x->0) (a+bx sin x + c cosx)/x^4=2` then a=, b=, c=

Text Solution

Verified by Experts

`lim_(x->0) (a+bxsinx+c cosx)/x^4 = 2`
Here, we will use,
`sinx = x-x^3/(3!)+x^5/(5!)+...`
`cosx = 1-x^2/(2!)+x^4/(4!)+...`
So, given equation becomes,
`lim_(x->0) (a+(bx^2-(bx^4)/6+...)+(c-(cx^2)/2+(cx^2)/24+...))/x^4 = 2`
Now, terms of `x` with power less than `4` and more than `4` will be `0` .
`:. a+c = 0=> a = -c->(1)`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

If lim_(x->0) (a + b sin x-cosx + ce^x)/x^3 exists, then the value of a + b + c is

If lim_(x->0) (a + b sin x-cosx + ce^x)/x^3 exists, then the value of a + b + c is

lim_(x rarr0)(sin x+cosx)^(1/(2x))

If lim_(x to 1) (ax^(2)+bx+c)/((x-1)^(2))=2 , then (a, b, c) is

If lim_(x rarr0)(cos x+a sin bx)^((1)/(x))=e^(2), then (a,b) is equal to

If lim_(x→0) ​ (x^asin^b x)/(sin(x^c)) , where a , b , c in R ~{0},exists and has non-zero value. Then,

If lim_(x→0) ​ (x^asin^b x)/(sin(x^c)) , where a , b , c in R ~{0},exists and has non-zero value. Then,

If lim_(x rarr0)(a cos x+bx sin x-5)/(x^(4)) is finite the a=

lim_(x->0) (1-cos x cos 2x cos 3x)/ (sin^2 2x) is equal to a) 3/4 b) 7/4 c) 7/2 d) -3/4

lim_(x->0) (1-cos x cos 2x cos 3x)/ (sin^2 2x) is equal to a) 3/4 b) 7/4 c) 7/2 d) -3/4