Derivative of Standard Functions

Q. f(x)+f(2x)+f(2-x)+f(1+x)=x ∀ x∈ R, then the value of f(0) is_________

Q. solve for x: (x^2- 6x+3) (x^2-6x -2)≥slant 50

Q. The value of (-1+i root3)^1008+(-1-i root3)^1008

Q. 10.The values of x for which function f(x)= cos(2x+pi/4) is decreasing are a) (-pi/8, pi/8)

Q. If the line px+qy=r intersects the ellipse x^2+4y^2=4 in points, whose ecentric angles differ by 60 degree, then r^2 is equal to (1) 3/4(4p^2+q^2) (2) 4/3(4p^2+q^2) (3) 2/3(4p^2+q^2) (4) 3/4(p^2+4q^2)

Q. if f(x)=3x+5.g(x)=6x-1 then find a)(f+9)(x) (b)(f-9)(2) (c)(f9)(3) (d)(f/9)(x) and its domain

Q. if the line lx+my+n=0 is a normal to the ellipse x^{2 }/a^2+y^2/b^2=1, then find the conditio

Q. { The domain of }f(x)=\sqrt{1-2\sqrt x+x} is

Q. If f(x) = ax + b and f(0) = 2 and f '(0) = 1, then the value of f(2) is

Q. x(x^{n-1}-nα^{n-1})+α^n(n-1)is divisible by (x-α)^2for (A)n>1 (B)n>2(c)all n∈ N (d)none of these

Q. let f(x) be a function such that f(x).f(y)=f(x+y), f(0)=1, f(1)=4.If 2g(x)=f(x)(1-g(x)) then find g(x)+g(1-x)

Q. 36. If f(X+1/y) + f(x-1/y)=2f(X)f(1/y) for all X, y belong to R-{0} and f(0)=1/2 then f(4) is

Q. f(m+n)=f(mn) and f(2^1/2)=18 then find the value of f(2020)

Q. if alpha and beta are the complex cube root of infinity prove:- (1+alpha)(1+beta)(1+alpha sq)(1+ beta sq)=1

Q. The range of the function $f\left(x\right)=\ln \left({\sin }^{-1}\right(x^2+x\left)\right),$ is

Q.

If $y$ = $(1+x)(1+x^2)(1+x^4)....(1+x^{2n})$, then $\frac{dy}{dx}$ at x = 0 is

1. 0

2. -1

3. 1

4. 2

Q. If alpha and beta are the roots of the equation x^2+6x+lamda=0 and 3alpha+2beta=-20, then lamda=

Q.

If $y^2$ = $a{x}^2+bx+c$, then $y^3.\frac{d^{2}y}{d{x}^2}$ is

1. a constant

2. a function of y only

3. a function of x only

4. a function of x and y

Q. Solve the equation(value of x): \operatorname{cos}^2x+\sqrt3=2(\sqrt3+1)

Q. 9.ax +b

Q.

$\text{If}y=2^{2^x},then\frac{dy}{dx}=$

1. 

2. 

3. 

4. 

Q. The set of values of x satisfying (x^2-x-1)(x^2-x-7) < -5 is (a, b) U (c, d) then a+b+c+d is equal to (1)0 (2)1 (3)2 (4)4

Q. If $x^4+\frac{1}{x^4}=322$, then find the value of $(x^3-\frac{1}{x^3})$.

1. $109$
2. $105$
3. $100$
4. $76$

Q. Let f(x) = 2x + 5 and g(x) = x² + x. Describe (i) f + g (ii) f − g (iii) fg (iv) f/g. Find the domain in each case.

Q. 9.Find the derivative ofG) 2r-34(in (5x3. 3x-1) (x-1)(iv) r 3-6x(vi)-9x-"(5+3x)(iii)(v) x4(3-4x-x3x-1

Q. 11. 4/x-2

Q.

$\frac{d}{dx}\left\{x^{1/x}\right\}=$

1. 

2. 1+logx

3. 

4. 

Q. 29. f(1)=2 , g(1)=2, f(x), g(x) exist then, value of lim x->1 [( f(1)g(x)-f (1)-g (1)f (x)+g (1))/(f (1)g(x)-f(x)g(1))]

Q. The value of (1 + i)(1-i^2) (1+i^4)(1-i^5) is

Q. ax+bcx+d5.