Question

If f(x) = 5^x+5^-x-3
/x^2 forx=0=k


continuous at x=0 Find k​

Answer 1

Step-by-step explanation:

x)=

⎩

⎪

⎨

⎪

⎧

5x

log(1+3x)

,forx



=0

k,forx=0

Given f(x) is continuous at x=0⇒

x→0

+

lim

f(x)=

x→0

−

lim

f(x)=f(x)

h→0

lim

5(0+h)

log(1+3(0+h))

=

x→0

−

lim

5(0−h)

log(1+3(0−h))

=k

⇒

h→0

lim

5

1+3h

1

.(3)

=

h→0

lim

−5

1−3h

1

(−3)

=k (L' Hospital Rule)

⇒

5

3

=

5

3

=k

⇒k=

5

3