f(x) b-a dx = 2 Prove f(x)+f(a+b-x) a

Q: За. (a) Differentiate x³ + x. (b) Use the Fundamental Theorem of Calculus to find (3x² + 1) dx.

A: Fundamental theorem of calculus: 1. If f is a continuous function on closed interval [a,b] and F be…

Q: ction f(x)=-

A:

Q: Let f(x, y) = ln(x + y − 1). Then, ƒ(e, 1) =

A:

Q: sin(t) dt , 1-4x 1+ t2 4 If f(x) then f' (x) =

A:

Q: b) I =f- x(1+(In x))

A:

Q: f(x) = 'dt th (2) 3=

A:

Q: dy Prove that dx of x2 +2x is f'(x)=2x + 2

A:

Q: .4 -1 sec J2 Evaluate x dx

A:

Q: (213 -1 28 dt dz

A:

Q: G. (CHAIN RULE) 1. f(x) = (3x² - 2x+4)² 2. y = sin 2x 4 (a² - y²)² 4. g(x)= (3x² + 4x - 5)5 3. 2 =

A:

Q: V3x-e2x-(x ln x)(ln(ln x))| In(ln x) Given a function, y = dy Show that dx V3x-e2x (x In…

A:

Q: Use chain rule to find express answer in terms of x only. dx y = Vu² – 1 u = 4Vx

A:

Q: Using Beta function, show that dx 3- (b – x) (x – a) |

A:

Q: a) Find the directional derivative of S = In(2x +3y) at point (-1,1) in the direction ef 4i - 3i

A: The directional derivative of a function f(x, y) in the direction of the unit vector (a, b) is given…

Q: et f(x) = x3- 3x2-1,  x ≥ 2. Find the value of df-1/dx at the point x = -1.

A: Let f(x) = x3- 3x2-1,  x ≥ 2. Find the value of df-1/dx at the point x = -1.

Q: f(x) = 2 arctan x + x %3D

A: f(x)=2arctan(x)+x

Q: 75. Show that (x – a)f(x) dx. f(t) dt ) dx

A:

Q: f (x) = cos(x) f(x) = tan(sin(x)) g(x) = In(2x2 + 4x + 3)

A:

Q: rsin x 3. F(x) = f* Vi dt %3D 3.

A:

Q: Let f(x, y) = ln(x + y − 1). Then, ƒ(1, 1) =

A: The given function is;  f(x,y)=ln(x+y-1).

Q: dx Show that f - In|ax + b| + C where a # 0. ax+b

A:

Q: x(T-X) ○<Xくす f(x)= -Tく×<。 X(T+x) -T<Xへp

A: Given that f(x)=x(π-x),                  0&lt;x&lt;πx(π+x),                  -π&lt;x&lt;0 To find…

Q: ,x € (0, 2] ,a = 0 f(x) = sinx then f (x) dx = 1 3 2.

A:

Q: f(x, y) = 9xye(x² + y²) f(0, 0) = f(0, 1) = = f(1, 1) = ==== f(-1, -1) =

A:

Q: Find linearizing ( L(x) ) f(x) at x=a . where f(x) = tanx and a = π a) π b)  x - π c) π - x d)…

A: SOLUTION-

Q: Limit -1 to 1 integral (1-1/2 x) dx

A: Given:        ∫-111 - 12x dx   To find the value of ∫-111 - 12x dx   Formula:          ∫xn dx = xn…

Q: tanx -√ S sec²x 1+ et tanx In (secx) √✓ 1+tan²x 1+ elanx sec ³x 1+etanx If f(x) = A B (с 1+1² 1+e'…

A:

Q: e -e Vx x +0 Let f(x) = D3 /x +eVr x =0 xDx 0.

A: We can find the function f(x) is continous or not and differentiable or not by following the below…

Q: 3 Let f(x) = 8x° 1 df 15x - 5, x2 1.5. Find the value of dx at the point x= 2004 = f(7). %3D

A: Known fact: derivative of f-1x=1f' f-1x.

Q: 71. Prove the reduction formula tank x dx = tan" k-1 х | tank-2 x dx k – 1 Hint: tank x = (sec² x –…

A:

Q: Find the limits

A: Consider the provided expression, limx,y→0,4xy Find the limit of the provided expression.

Q: (sin (x))2 dx V1-x2

A: The given integral is

Q: 10 If f (x) dx -7 and f (x) dx = 1 then determine -3 -3 10 [1- f(2) dz 5 showing working.

A: Given: ∫-35f(x)dx=-7 and ∫-310f(x)dx=1

Q: 6 X, 一T Sx< 0, 10, f(x) = %3D f(x+27) = f(x) 0 <x < T;

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: sint F(x) = √"* ( *ª*** ( √ ¹ + uª) du) dt Jo

A: The Fundamental Theorem of Calculus says: F(x)=∫ag(x)f(t) dt⇒F'(x)=f(g(x))g'(x)

Q: sin(bx)+a x<0 f(x)=< | sin (2x)+2x x20 which is differentiable everywhere, then what are values of a…

A:

Q: g(=) = / Compute the derivative of g(x) dt. -2xe5 - 2xe - 2xe

A: Given           g(x) = ∫x21et3 dt

Q: f(x) is a twice differentiable function with f(0) = 4, ƒ(1) = 3, f'(1) = 6, Then So 3xf" (x)dx =

A:

Q: 1-2 c) dx

A: Evaluate the integral: ∫01e1-xdx. Simplify- ∫01e·e-xdx Apply ∫afx dx = a∫fx dx here a is constant.…

Q: sin(2x3 +3y3) If f(x,y)= 5330x2+2665y2 (x,y)# (0,0) then (x,y)=(0,0)

A: Given,             fx,y=sin2x3+3y35330x2+2665y2x,y≠0,00x,y=0,0

Q: sin(2x3 +3y³) If f(x,y)= 5744x2+2872y2 (x,y)# (0,0) then (x,y)=(0,0) fx(0,0)= f,(0,0)=

A:

Q: Let f (2) = (4z + 3) (i – 2). What is the real part of the derivative f' (1+ i)?

A: A complex-valued function consists of two parts. The part without i is referred to as the real part.…

Q: sech x+csch x Q3: prove that e2x %3D csch x-sech x

A:

Q: t-a lim xa x- a dt sin(t - a)

A:

Q: Evaluate using Theorem - f(x) dx f(x) dx + | f(x)dx = |1 – e*|dr

A: Here The Given function is  f(x)=1-exand we have to evaluate∫-221-exdx

Q: f(x) = tan (2x5 – x) %3D f'(x) = 9хcosx f(x) = %3D csc(x) f'(x) = %3D f(x) = ex f'(x) = %3D e5x+3 y…

A:

Q: 1 3 + e2 + dx 2 (3х)3 2х2

A: The integral is ∫13x3-32x2+e2+x2dx. Evaluate the integral using u-substitution as follows.…

Q: sin(2x²)+x³ . Let f(x) = 0, df if x + 0 Then find- if x = 0 dx x=0

A:

Q: ppose f(x)= -cosx-4). Evaluate dx

A:

Q: 5-7 -1 Using quotient rule, show-that d [cotx] dx 2. 1+x

A: