Q14 of 45 Page 1

Find the value of ‘a’ for which the function f defined as


is continuous at x = 0.

If f is a real function on a subset of the real numbers and c be a point in the domain of f, then f is continuous at c if limx→c f(x)=f(c).


Since the function is continuous at x=0


LHL = RHL


LHL:




= a× 1


= a


RHL:




∵ cos 2x = 1 – 2 sin2x





= 1/2


Hence the value of a is .


More from this chapter

All 45 →
12

Prove the following:


OR


Find the value of

13

Using properties of determinants, prove that

 15

Differentiate

OR


If x = a(θ – sin θ), y = a(1 + cosθ), find

 16

Sand is pouring from a pipe at the rate of 12 cm3/s. The falling sand forms a cone on theground in such a way that the height of the cone is always one-sixth of the radius of the base.How fast is the height of the sand cone increasing when the height is 4 cm?

OR


Find the points on the curve x2 + y2 – 2x – 3 = 0 at which the tangents are parallel to x–axis.