निम्नलिखित प्रश्नो के मान ज्ञात कीजिये :
(i) ` lim _( x to 1)(x^(10)+x^(5)+1)/(x-1)` (ii) `lim _( theta to 0 )(sin. theta/4)/theta`

lim _( theta to 0) ( sin 5theta)/( tan 4theta)

lim_(x rarr theta)(sin theta-sin x)/(x-theta)

Prove that lim_(thetararr0)(sin theta)/(theta)=1 .

lim_(theta rarr 0) (1-cos theta)/(theta sin theta) =

Evaluate lim_(theta rarr 0) (1-cos 4theta)/(1-cos 5theta)

lim_(x rarr0)(sin^(3)theta*tan^(3)theta)/(theta^(6))

Evaluate the following limits (i) lim_(x to (pi)/(2)) tan^(2) x [sqrt(2 sin^(2) x + 3 sin x + 4) - sqrt(sin^(2) x + 6 sin x + 2)] (ii) lim_(theta to 0) (sqrt(1 + sin 3 theta) -1)/(ln(1 + tan 2theta)) (iii) lim_(x to 0) (sqrt(1 + x) - ""^(3)sqrt(1 + x))/(x) (iv) lim_(phi to 0) (8)/(phi^(8)) (1 - cos (phi^(2))/(2) - cos (phi^(2))/(4) + cos (phi^(2))/(2). cos (phi^(2))/(4))

Evaluate the following limits (i) lim_(x to (pi)/(2)) tan^(2) x [sqrt(2 sin^(2) x + 3 sin x + 4) - sqrt(sin^(2) x + 6 sin x + 2)] (ii) lim_(theta to 0) (sqrt(1 + sin 3 theta) -1)/(ln(1 + tan 2theta)) (iii) lim_(x to 0) (sqrt(1 + x) - ""^(3)sqrt(1 + x))/(x) (iv) lim_(phi to 0) (8)/(phi^(8)) (1 - cos (phi^(2))/(2) - cos (phi^(2))/(4) + cos (phi^(2))/(2). cos (phi^(2))/(4))

(a) Let f,g : R to R be defined as f(x) =2x -|x| and g(x) =2x + |x| . Find fog. (b) Prove that lim_(theta to 0) (sin theta)/theta =1