(a) Compute /(2) dr, given that f(b) 3 and that | af'(a) dr b(1 + f(-b)). (b) Computei (2) dz. given that h(b) = 6, h(-b) -6 and that j(x) = xh'(x) is an odd

Q: Prove that 1 + p'2 p4 where primes denote differentiation with respect to 's'. 1. x"2 + y"2 + z"2 %D

A:

Q: 2. Evaluate the integral 4 dx V2x-5 5/2

A:

Q: 1 x+1 Integrate: r21?

A: Here we have, I=∫01x+1x2+2x2dx

Q: 2. Let f(x, y, z) = In(x² + 2) + y²e#* - cos(2yz). Find fzyz-

A:

Q: 1 (b) Evaluate the integral S ; dx 2x2-12x+26

A: To evaluate: The integral of . Formula used: Integration Formula:

Q: Prove 8xyz < (x + y)(y + z)(x + z) for every x, y, z E [0, +∞[.

A: We have to prove given identity: Concept:

Q: 3. Find an orthonormal pair one of whose members is proportional to (4, -3).

A:

Q: .Prove that e- -dt < (1+ t²)* 1/4 6.

A:

Q: Find the Tians Farm F(s) = "suy (27>1>0) (1 – s)(1 – e **) 3) f(1) = e',

A: Given problem:- Find laplace transformation of f(t) =et (0&lt;t&lt;2π)

Q: Suppose that a consumer derives his utility from two goods, the amounts of which are x and y,…

A:

Q: The integral of the given function ∫csc^6(x) dx is equal to

A: Need to find ∫cosec6(x) dx

Q: Integrate the function. 16x +즐 + C V16 -2 8 sin 1 +C 2 V16-2 +C + 16V16 - x2 8x - W16-2 +C

A:

Q: Evaluate the integral: f sin 7x cos 2x dx. A) sin 5x + sin 9x + c. 2 B) cos 5x +co cos 9x + c. 10 C)…

A:

Q: 3 Evaluate the integral: dx 2 Vx -1

A:

Q: 1.1 the integral f cos(lnx) dx . x2 1.2 the integral S x³V1– 2x dx

A: 1.1 Given integral is ∫coslnxx2dx Let u=lnx⇒dudx=1x dx=xdu1x=e-u∫e-ucosudu we will integrate by…

Q: (2x+4) + 1 x² +2x- 10 dx = x² (x² + 4x +5) (2x +4) +1) dx- x² + 4x+5, Consider dx evaluate | x² + 4x…

A:

Q: B. Let z- ( x-y)exy Show: Zxx + zyy + e x9 Cy 3- x³)- -z (xy+ 2)

A: Given that                       z=(x-y)exy

Q: 3,2 Evaluate the integral xx + x +2 dx%3D

A:

Q: 1 Evaluate the improper intergal | dx (x2 + 9)° using the residue theorem.

A:

Q: 2. Find the linearization of the function f(x, y) = In(x³y®) at the point (xo, yo) (4, 3). Leave all…

A: Consider the following function: fx,y=lnx3y6 fxx,y=ddxlnx3y6=1x3y6×3x2y6=3x…

Q: Verify Young's Theorem In(2x + y) y2 x2 + + e(x+2y)

A:

Q: Find the total differential z = 5x3y2

A: The given function is z=5x3y2. Total differential: Let z=f(x,y) be continuous on an open set S. Let…

Q: 1 Verify Eular's theorem for z=- =(x²+xy+y*)' x²+xy+y² 2

A: The expression z=1x2+xy+y2=x2+xy+y2-1. We have to verify the Euler's Theorem.

Q: the Fundamental Theorem of Ca -5 (x³ – 9x)dx. v3

A: Here we have to use fundamental theorem of calculus to find the exact value of  ∫05(x3-9x)dx…

Q: 4. Using the definition of sech x ,x 0 in terms of e , prove that 1+V1-x2 sech x = In ,0<x <1 Hence,…

A: 4) i)

Q: (b) Prove that sint -dt > 0 t+1 for all a > 0.

A: Given:- ∫0x sintt+1dt &gt;0

Q: S de x² –2 x+1 A x2 --x - In Ix + 11 + C C x2 +x - In Lx + 11 + C B x² -x + In Lx + 11 + C x2 +x +…

A: Given ∫x2-2x+1dx. The objective is to evaluate the integral.

Q: - Find the total differential df of f (x, y) = (x² + y²) 3/2.

A:

Q: 2. Use the linear approximation of f(x) = x² ln(x + 1) to estimate (1.01)² ln(2.01).

A: We need to estimate value.

Q: 5- Find the tangent (slope) of the function f(x) = x3 - 6x2 + 12x +8 when x = 6- Find the results of…

A: Since question 6 is graded so as per company's rule, i can't answer any graded question. So i answer…

Q: 8. Compute using the trig. substitution S x2 -dx (1–x²)1/2

A:

Q: 8x + 1 10. Evaluate the integral / dx. 4.x2 + 12x + 10 11 (a) In |4.x2 + 12x + 10|| tan-(2x + 3) + C…

A:

Q: Find the general solution to the DE using the method of Variation of Parameters: у" - Зу" + Зу'…

A:

Q: (6) Find the indefinite integral (af* -3x +2 Fdx x+1 12x - 22x (bJ -dx 3x* -11x +15 x² + 2x +3 -dx…

A: Note: As per companys policy we should do maximum 3 subparts of a question.So, kindly post the other…

Q: S x2 +2x-10 (2x+4) + 1 JE + 4x +5) Consider dx = x² (x² + 4x + 5) (2x+4) + 1 dx- x² + 4x +5 dx ,…

A:

Q: 39. (a) Show that 1 1 > 0 2x V1+x² for x > 1. (b) Use your result in (a) to show that 1 dx 1+x is…

A: The compleet solutions are geven below

Q: Find the integration inner product on C[-4, 3] of the given functions. f(x) = 16x g(x) = 2x?

A:

Q: Find the total differential of z = In (2x – 3y).

A:

Q: Suppose that x2 = y2 = e and yz = zxy. Show that xy =yx.

A: Since, yz = zxy

Q: Consider the IVP S2(t) = -1+cos(t + x(t)) cos(t + x(t)) x(0) = 0. Show that the ODE is exact and…

A:

Q: By the Fundamental Theorem of Calculus: •t „2 +1 dx 5x +1 d dt d and dt - 6t x2 +1 dx 5x +1 d…

A: Given

Q: 1. A force of F (x) 2x = xe + 6x – 2 acts on an object. What is the work required to move the object…

A:

Q: 4. Prove 1 < | V1+ a dx <2 0,

A:

Q: If f(x) > g(x) >0 for X in [1,0) and g(x) dx diverges to +0, then | F(x)dx also diverges to +. True…

A: It is TRUE, that 0&lt;g(x)≤f(x) for x in [1,∞)  and                               ∫1∞g(x)dx diverges…

Q: 1 Evaluate the improper intergal dx (x² + 16)² using the residue theorem. 8.

A:

Q: 4. Prove that ах x" ea" dx xn- п-1 ‚ax dx а а

A:

Q: 5. prove that d (-x) (+ x) = X dx dx d² dx² - x² +1

A:

Q: 19. Consider the integral f√x²+25 dx. 9x² a. In/√x² + 25 +x/- - b. x+ In/√x² + 25/+ √x²+25 9x √x²+25…

A: Solve the integral  √(x2+25)/9x2

Q: Suppose that x2 = y2 = e and yz = zxy. Show that xy = yx.

A: Assume that x2 = y2 = e and yz = zxy.  Now from  yz = zxy we have  yz-1 = zxy-1z-1y-1 = y-1 x-1 z-1…