Let f and g be real-valued functions. If \lim_{x\to0} {2f(x)-g(x)}/(f(x)+7)^{2/3} = 7/4 , \lim_{x\to0} f (x) = 1 and \lim_{x\to0} g (x) = α , then h (x) = \\begin{array}{cc}\sin (\alphax) & 0 \leq x \leq \pi/{10\end{array} ; \cos(2\alphax) , \pi/{10}

Correct Answer is : continuous on [0,π5]

continuous at x = \pi/{10} only

TS EAMCET 06 May 2019 Shift 1 Solved Paper

Section: Mathematics

Question : 63 of 160

Marks: +1, -0

Let f and g be real-valued functions. If

lim

x→0

2f(x)−g(x)

(f(x)+7)

lim

x→0

f (x) = 1 and

lim

x→0

g (x) = α , then h (x) = {

sin(αx)

0≤x≤

cos(2αx)

<x≤

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