I Find the derivative of x2cos x-5- using first principle-ii For the function f x - left begin matrix a-b x- - x2lendmatrix right-llim x - 2 f x - f 2- Find the values of a and b-

(i) x^2sin x+2x cos x (ii) a= 4/5 and b=12/5 ...

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Standard XI

Mathematics

Differentiability

i Find the de...

Question

(i) Find the derivative of $x^{2} c o s x + 5$ , using first principle.

(ii) For the function $f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} a + b x, & x < 2 4, & x = 2 b - a x, & x > 2 \end{matrix}$

${lim}_{x \to 2} f (x) = f (2)$ . Find the values of a and b.

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Solution

$(i) - x^{2} s i n x + 2 x c o s x$

$(i i) a = \frac{- 4}{5} a n d b = \frac{12}{5}$

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(i) Find the derivative of x2cos x+5, using first principle. (ii) For the function f(x)=⎧⎪⎨⎪⎩a+bx,x<24,x=2b−ax,x>2 limx→2f(x)=f(2). Find the values of a and b.

(i) −x2sin x+2x cos x (ii) a=−45 and b=125

(i) Find the derivative of $x^{2} c o s x + 5$ , using first principle.

(ii) For the function $f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} a + b x, & x < 2 4, & x = 2 b - a x, & x > 2 \end{matrix}$

${lim}_{x \to 2} f (x) = f (2)$ . Find the values of a and b.

$(i) - x^{2} s i n x + 2 x c o s x$

$(i i) a = \frac{- 4}{5} a n d b = \frac{12}{5}$