Lim h - 0a-h2sin a-h-a2sin a-h-A- a cos a-a2sin aB- a sin a-a2cos aC- 2 a sin a - a 2cos aD- 2 a cos a - a 2sin a

The correct option is C 2a sin a+a^2 cos ad/da [a^2 sin a]=2a sin a+a^2 cos a Aliter: Apply L Hospital's rule, lim_h → 0(a+h)^2 sin (a+h) a^2 sin a/h = lim_h ...

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Byju's Answer

Standard XII

Mathematics

Range of Trigonometric Expressions

lim h → 0a+h2...

Question

${lim}_{h \to 0} \frac{(a + h)^{2} s i n (a + h) - a^{2} s i n a}{h} =$

a c o s a + a^{2} s i n a

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a s i n a + a^{2} c o s a

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2 a s i n a + a^{2} c o s a

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2 a c o s a + a^{2} s i n a

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Solution

The correct option is C $2 a s i n a + a^{2} c o s a$
$\frac{d}{d a} [a^{2} s i n a] = 2 a s i n a + a^{2} c o s a$
Aliter: Apply L - Hospital's rule,
${lim}_{h \to 0} \frac{(a + h)^{2} s i n (a + h) - a^{2} s i n a}{h}$
$= {lim}_{h \to 0} \frac{2 (a + h) s i n (a + h) + (a + h)^{2} c o s (a + h)}{1}$
$= 2 a s i n a + a^{2} c o s a$

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limh→0(a+h)2 sin(a+h)−a2 sin ah=

The correct option is C 2a sin a+a2 cos adda[a2 sin a]=2a sin a+a2 cos a Aliter: Apply L - Hospital's rule, limh→0(a+h)2sin(a+h)−a2 sin ah =limh→02(a+h)sin(a+h)+(a+h)2cos(a+h)1 =2a sin a+a2 cos a

${lim}_{h \to 0} \frac{(a + h)^{2} s i n (a + h) - a^{2} s i n a}{h} =$