Home
Class 12
MATHS
Evaluate lim(yto0)(y^(2)+sin x)/(x^(2)+s...

Evaluate `lim_(yto0)(y^(2)+sin x)/(x^(2)+siny^(2)),` where `(x,y)to(0,0)` along the curve `x=y^(2)`.

Text Solution

Verified by Experts

The correct Answer is:
2
`underset(yto0)underset(xto0)lim(y^(2)+sin x)/(x^(2)+siny^(2))=underset(xto0)lim(x+sinx)/(x^(2)+sinx)=underset(xto0)lim(1+(sinx)/(x))/(x+(sinx)/(x))=2`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE|Exercise Exercise 2.6|9 Videos

  • LIMITS

    CENGAGE|Exercise Exercise 2.7|7 Videos

  • LIMITS

    CENGAGE|Exercise Exercise 2.4|5 Videos

  • JEE 2019

    CENGAGE|Exercise Chapter 10|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

Evaluate: lim_(x rarr0)(y^(2)+sin x)/(x^(2)+sin y^(2)) where (x,y)rarr(0,) along the curve x=y^(2)

Q.lim_(x rarr0,y rarr0)(y^(2)+sin x)/(x^(2)+sin y^(2)), when (x,y)rarr(0,0) along the curve x=y^(2) is

Evaluate : lim_(x rarr0)((x^(2)+sin x^(2))/(x^(2)+x^(3)))

Evaluate lim_(x rarr0)(2sin x-sin(2x))/(x^(3))

At (0,0) the curve y^2=x^3+x^2

the value of lim_(x rarr y)(sin^(2)x-sin^(2)y)/(x^(2)-y^(2)) equals

A curve satisfies the differential equation (dy)/(dx)=(x+1-xy^(2))/(x^(2)y-y) and passes through (0,0)(1) The equation of the curve is x^(2)+y^(2)+2x=x^(2)y^(2)(2) The equation of the is a tangent to curve (4)y=0 is a tangent to curve

If x^(2)+x=1-y^(2) , where x gt 0, y gt 0 , then find the maximum value of x sqrt(y) .