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find x 0 f x and x 1 f x where 2x 3 x 0 3 x 1 x 0
Question:
Find
\(\lim_{x\rightarrow 0}\)
f(x) and
\(\lim_{x\rightarrow 1}\)
f(x) where { 2x+3, x≤0 3 (x+1), x>0
CBSE Class XI
Updated On:
Oct 23, 2023
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Solution and Explanation
The given function is
f(x) = { 2x+3, x≤0 3(x+1) x>0
\(\lim_{x\rightarrow 0^-}\)
f(x) =
\(\lim_{x\rightarrow 0}\)
[2x+3] = (2(0)+3=3
\(\lim_{x\rightarrow 0^-}\)
f(x) =
\(\lim_{x\rightarrow 0}\)
3(x+1) = 3(0+1)= 3
∴
\(\lim_{x\rightarrow 0^-}\)
f(x) =
\(\lim_{x\rightarrow 0^+}\)
f(x) =
\(\lim_{x\rightarrow 0}\)
f(x) = 3
\(\lim_{x\rightarrow 1^-}\)
f(x) =
\(\lim_{x\rightarrow 0^+}\)
3(x+1) = 3(1+1) =6
\(\lim_{x\rightarrow 1^-}\)
f(x) =
\(\lim_{x\rightarrow 1}\)
3(x+1) = 3(1+1) =6
∴
\(\lim_{x\rightarrow 1^-}\)
f(x) =
\(\lim_{x\rightarrow 1^+}\)
f(x) =
\(\lim_{x\rightarrow 1}\)
f(x) = 6
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