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+1 vote
25.6k views
in Mathematics by (34.9k points)

Let f : R → R be a function defined as

\(f(x)= \begin{cases} \frac{sin(a+1)x+sin\,2x}{2x}&, if\,x<0\\ \,\,\,\,\,\,\,\,\,\,\,\,b&,if\,x=0\\ \frac{\sqrt{x+bx^3}-\sqrt x}{bx^{5/2}}&,if\,x>0 \end{cases} \)

If f is continuous at x = 0, then the value of a + b is equal to:

(1) \(-\frac 52\)

(2) -2

(3) -3

(4) \(-\frac 32\)

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1 Answer

+1 vote
by (34.4k points)

Correct option is (4) \(-\frac 32\)

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