If f(x)=-2sinx if x≤-π2Asinx+B if -π2

If $f (x) = \{\begin{matrix} - 2 \sin x & if & x \leq - \frac{π}{2} \\ A \sin x + B & if & - \frac{π}{2} < x < \frac{π}{2} \\ \cos x & if & x \geq \frac{π}{2} \end{matrix}$
is a continuous function then

A
$A = 1, B = - 1$
B
$A = - 1, B = 1$
C
$A = 0, B = 2$
D
$A = - 2, B = 2$

Solution:

$f (- \frac{π}{2}) = - 2 \sin (- \frac{π}{2}) = 2$

$\lim_{x \to \infty} f (x) = \lim_{x \to \infty} (A \sin x + B) = - A + B$

so $2 = - A + B \dots (i)$

Also $f (\frac{π}{2}) = \cos \frac{π}{2} = 0$

$\lim_{x \to \frac{π}{2} -} f (x) = \lim_{x \to π / 2 -} (A \sin x + B) = A + B$

Hence A + B = 0 (ii)

Solving (i) and (ii), we get $A = - 1, B = 1$ .

Related content

Genetics and Evolution | Mind Map

Kerala NEET UG Merit List 2023

NEET Exam Centres in Hyderabad 2024

Ecology & Environments

NEET Exam Centres in Maharashtra 2024

CBSE Biotechnology and its Applications Class 12 Mind Map for Chapter 10 of Biology, Download PDF

NEET Exam Centres in Tamil Nadu 2024

NEET Exam Centres in Karnataka 2024

Microbes in Human Welfare Class 12 Mind Map- Check Characteristics, Classification, Functions & Examples

NEET Exam Centres in Gujarat 2024