Question

02] Find the value of k if the following functions are continuous at given point, a) f(x) = (10 ^ x - 5 ^ x - 2 ^ x + 1)/(x ^ 2) if x=\=0 at x = 0; =klog 2, if x = 0​

Answer 1

Answer:

As f(x) is continuous at x=2

lim

x→2

+

f(x)=lim

x→2

+

(3x−1)

=3×2−1=6−1=5

And lim

x→2

−

f(x)=lim

x→2

−

(2x+1)

=2×2+1=4+1=5

⇒f(2

−

)=f(2

+

)=k since f is continuous at x=2

∴k=5