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CBSE Class 12 Math 2022 Term I Solved Paper

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Question : 12
Total: 50
The function f(x)={
‌
e3x−e−5x
x
‌‌ if ‌x≠0
k‌ if ‌x=0
. is continuous at x=0 for the value of k, as
Solution:     👈: Video Solution
Explanation: Since, f(x) is continuous at x=0, then
LHL=RHL=f(0)‌ or ‌LHL=RHL=k
Now,
LHL=
lim
h→0
‌
e3(0−h)−e−5(0−h)
0−h

=
lim
h→0
‌
e−3h−e5h
−h

=
lim
h→0
(‌
e−3h−1
−h
)+
lim
h→0
(‌
e5h−1
h
)
=3
lim
h→0
(‌
e−3h−1
−3h
)+5
lim
h→0
(‌
e5h−1
5h
)
=3×1+5×1=8
‌ Thus, ‌‌‌k=8‌. ‌
‌
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