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Syllabus

derivative using first principle -

sin_/x

(sin under root x)5) From a group of 8 children, 3 girls and 5 boys, 3 children are selected at random. Calculate the probabilities that the selected group contain

(i) no girl

(ii) only one girl

(iii) only one particular girl (iv) at least 1 girl (v) more girls than boys

Differentiate sinx/x from the first principle.

^{4}xIf x root (1+y) + y root (1+x) = 0

Prove that dy/dx = -1/(1+x)

^{2}experts do help!!

$\underset{x\to 3}{\mathrm{lim}}\frac{\sum _{r=1}^{n}{X}^{r}-\sum _{r=1}^{n}{3}^{r}}{x-3}$

derivative of 1)logx by first principle

^{3}x-3tan^{2}x+12tanx +3, $\in (0,\frac{\pi}{2})$ is,(A) increasing (B) decreasing

(C) increasing in (0, $\pi /4)anddecrea\mathrm{sin}gin(\pi /4,\pi /2)$

(D) none of these

find the derivative of

Find the derivative of root tanx from first principles.

evaluate:

lim x-0 [1-cosx (cos2x)^1/2] / x^2

how can we derivate cosecx by first principle

lim x tends to 4

x-4 / 3- root 13 - x

lim x tends to zero 1-cos4x / x

^{2}?a) y = 3sin

^{2}x - sin^{3}xb) y = (tan

^{3}x)/3 - tanx + xc) y = xsec

^{2}x - tanxFind

^{-1}by using product rule, and quotient rule respectively. Verify that the answers obtained are the same.find dy/dx if y = 1/(ax + b)

find the dervative of

find derivative of log(cosx) w.r.t. 'x' using 1st principle

Find derivative of sin2x,cos2x and tan2x using first principle

derivative of sin^n x

derivative of square root of cos x by first principle

lim. x->0

1- cosx.cos2x.cos3x /sin

^{2}2xFind dy/dx. If (x

^{2}+ y^{2})^{2}= xywhat is lim

_{x-0}x(e^{x}-1)/1-cosxdiscuss the continuity of function f(x)= |x|+|x-1| in interval [-1,2]

lim(x- -3) (x^2 - 9)/(root[x^2 + 16]-5)

y= x tanx / sec x +tanx

Q1: The function f:a to b defined by f(x) = - x

^{2}^{}+6x - 8 is a bijection if a and b belongs to which intervalQ2: If f(4) = 4 , f*(4) = 1 then lim x tends to 4 2-√f(x) / 2 -√x is equal to

lim cos2x - 1/cosx - 1

^{2}-10)find the derivative of cosx by first principle of derivative

evaluate lim h tends to 0 [ (a+h)^2 sin (a+h) - a^2sin a] / h

find derivative of sinX+cosX from first principle

rs aggrawal solutions

evaluate sin x - sin a / x-a?

lt.x--->0

3sinx -sin3x /x

^{3}lim tan x-sinx / sin

^{3}xx--0

evaluate lim x-pi/4 (cox-sinx)/(x-pi/4)

f(x)={1-coskx /xsinx ,x is not =0 and 1/2,x=0}

find k if limx-0f(x) = f(0)

log, then least value of x+y is:_{2}x + log_{2}y is greater than or equal to 6a) 4 b) 8 c) 16 d) 32

integrate x^6+1/x^2+1

evaluate limit x tends to pi/2 tan 2x / x-pi/2?

evaluate sin x - sin a / x-a?

^{2x }Sin3x Cos4x[ Hint given in the solution is 2sin3xcos4x = sin7x - sinx by std trignometry formulae

As i understand Sin2A = 2SinACosA . Therefore 2sin3xcos3x = sin6x

So as given in hint 2sin3xcos4x should it be corrected to2sin3xcos3x (cos3x in place of cos4x)

Correct me if i am wrong.]

Differentiate w.r.t x by using first principle

i)xcosx

cos3x + 3 cos x / ( pi /2 - x )^3

lim x-->0 (cos 3x-cos 5x)/x

^{2}Differentiate the following by using first principle -

i). tan (2x + 1)

ii).

√tan xiii). x

^{2 }sin x(a)1/root x , x not equal to 0

lim (x+y) sec (x+y) -x sec x / y

y--0

find derivative of :-

e

^{root cot x }by first principle ?

differentiate x2 cosx from first principle..

Evaluate:-

lim (x

^{4}-3x^{3}+2)/(x^{3}-5x^{2}+3x+1)x --1

Q=If a^{2}+ b^{2}=23ab,then prove that log(a+b/5) = 1/2 (loga + logb)Book Mathematics Class XI R.D.Sharma

Exercise 29.9, Qno- 29

Please send the solution

examine the continuity

f(x) =logx-log7/x-7 for x not equal to 7

=7 for x= 7 at x=7

tell me all the formulae of limits and derivatives of class 11th as well as 12th !!find dy/dx if y = log sinx.

Q. lim x tends to pi/2

1+cos2x / (pi-2x)

^{2}evaluate:

lim x-0 [(3^2x)-(2^3x)] / x

Differentiate using first principle : e

^{[under root(tan x)]}limit x tends to zero sinx-2sin3x+sin5x / x^3