5. Find two positive numbers whose sum is 10 and the sum of their squares is as small as possible.

Q: 3. da I² + 52 Integrate:

A: To solve the following problem

Q: sec(6z)tan(6x)dx, u = 6x

A:

Q: 4. Suppose U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {3, 4, 5, 6, 7}, B = {all multiples of 3} and C =…

A: U=1,2,3,4,5,6,7,8,9A=3,4,5,6,7B=all multiples of 3C=all multiples of 2

Q: A stone is dropped from the upper observation deck of a tower, 800 m above the ground. (Assume g =…

A:

Q: Find the first and the second derivatives of the function. y%3D 6-x

A: The given function is: y=x6-x  =-xx-6  =-x-6+6x-6  =-1+6x-6  =-1-6x-6

Q: 7.A Water font has a shape sp an inverfed arcular cone with ? base radius 4m nd herght m.lf water is…

A:

Q: Give the parametric and symmetric equations of the line that passes through the point (4, -3, 5) and…

A:

Q: If 7-4/3 = Vx-Vy, determine the values of x and y. %3D

A: We have to find the values of x and y from the above expression.

Q: dx Using Trigonometric Substitution J- , find f(0) = (x² + x + 1)7 O 3 sec? e 4 3 sec e 4 4 3 sec e…

A: The given integral,     ∫dxx2+x+132

Q: Using Integration By Parts, Vx In 2x dx =uv- -Svdu Jv du Find UV- du O 2 늘 xVX In 2x-| Vx dx Xx In…

A: A detailed solution is given below

Q: y Find dy/dx of eY sin y :

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: dx + (1 – x²)cot y dy = 0

A: Given problem :- dx + (1-x2 )cot(y) dy = 0 Find the general solution of given differential equation

Q: 5. Use differentials to approximate the value of V(3.01)² + 2(0.99) – 3 in four decimal places.

A:

Q: Use polar coordinate to evaluate (x² + y* )² dx dy . Leave your answer correct to two decimal…

A:

Q: The appropriate change of variables for the dx is Vx²-4 x=2 cosØ O x=2 sec Ø O x=2tan Ø O x=2 sineØ

A:

Q: 2. A solid right cylindrical cement block of volume 97 ft³ is to be made, and then painted except…

A:

Q: Evaluate csc°(3x)dx cot*(3x) cot (3x) cot(3x) + C 12 2 cot°(3x)_ 2cot³(3x)_ cot (3x) +C 15 9 O…

A:

Q: 4) y =iy ¡y' -x1

A:

Q: 3r + cos z Use Squeeze Theorem to evaluate lim VI+x² – 5x°

A: Given problem:-

Q: Using Integration By Parts, x sec - x tan x dx = %3D

A: Use integration by parts.

Q: (2х + 3у)dx + (у — х)dy —D 0

A:

Q: 3. x2 + 2ху + 3y?

A:

Q: 1 Using Integration By Parts, x sec x tan 2 1 -uv-Jvau Find u v- Svdu '2x sec 을x-J25ec을x dx o 1 2*…

A: From the given problem; ∫xsec12xtan12xdx=uv-∫vdu    ....1   We know that; ∫secxtanxdx=secx+C

Q: D 2x³ – x² + x +2 = (: find dx - A+B+C+D- Consider - + + + x+1 x4 + x3 O 2 O 4 O 3 O 5

A:

Q: ーx? + 4x +5 dx. Consider Using trigonometric substitution, what is the integral form in terms of

A:

Q: Vx In 2x dx=u v- v-fvdu Using Integration By Parts, Find Uv- du O 3 xVx In 23 2 12x- dx | O 2 Xx In…

A:

Q: Find the points on the ellipse 5x2 + y² = 5 that are farthest away from the point (1, 0). smaller…

A: To find the points on the ellipse 5x2+y2=5, that are farthest away from the point 1, 0.

Q: 2х dx cos?(2x) Evaluate 1. xtan (2x) + In|cos(2x)| + C 1 xtan (2x) + In|sec(2x)} + C xtan (2x) 1…

A:

Q: |(x² + a) 5 5x The resulting integral of dx is In +eTan-1X + C, where a, b, d, and e are integers.…

A: Given:        ∫5xx3+x2+4x+4dx Apply linearity:     =5∫xx3+x2+4x+4dx Factor the denominator:…

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 2 1 lim t++00 \ 5t2 + 6'4t (?, ?)

A:

Q: 2x3- x² + x + 2 dx = D dx find A+B+ C+D. + x+1 + Consider x4 + x3 4 O 3 O 2 O 5

A:

Q: The speed of a runner increased steadily during the first three seconds of a race. Her speed at…

A:

Q: lim(8x + 16) = 24 Use the epsilon-delta definition of limit to prove that æ→1

A: Let's find.

Q: 5x |(x²+ a) The resulting integral of dx is In +eTan-1X + C, where a, b, d, and e are integers. What…

A:

Q: Using Trigonometric Substitution  ∫ dx/ (x^2+x+1)^(3/2) find f theta

A:

Q: dx Using trigonometric substitution S = sin(0) + C, express the answer in terms of x. 3 (x²+x+1)7

A:

Q: .3 onsider the indefinite integral a - Va + 9 dr: This can be transformed into a basic integral by…

A: Given query is to transform the integral in u and du format.

Q: Find the antiderivative F of f that satisfies the given condition. Check your answer by comparing…

A: ∫f(x) dx=∫ 5-31+x2-1dx=∫ 5dx-∫ 31+x2-1dx=5x-3arctanxAdd a constant to the solution=5x-3arctanx+C…

Q: dy Solve for the general solution of the differential equation (ax+by+c)² where a, b, c e R dr and…

A:

Q: Use substitution to evaluate the integral. s1/5 sin(s/5 - 2)ds 1/5 6/5 sin(s - 2)ds = %3D

A:

Q: x² + x – 2 (3x – 1)(x² + 1)

A:

Q: Using Integration By Parts, x3 Vx² + 4 dx = u v- -Svau - Svdu- بی تر ر ترا Find UV- 3 1 .x2 (x2 +…

A:

Q: ntegrate 36(6 5) dr 3. Answer

A: Topic:- integration

Q: Q2/ solve the Differential Equation [ (2xy+3y²)dx = (x² + 2xy)dy ]

A:

Q: x² + x +2 dx - x2 – 1 Evaluate (х-1)2 + C x+1 x+ In- x+1 In- + C (x – 1)2 (x – 1)2 In- X+1 x+1 +C x+…

A:

Q: Evaluate the definite integral. sin(4t)dt

A: Here is the solution:

Q: 4. Given [2r + 5], 4- 2x 1² – 2x' if r < -1 f(x) = if –1<x< 2. sin(r – 2) 2 if r 22 a. Discuss the…

A:

Q: x² –9 dx Given: r3

A:

Q: 5xy = 4x²z – 3yz²; xz and xy.

A:

Q: x² + x +2 Evaluate x2 - 1 x+1 +C (x- 1)2 (x- 1)2 In- + C x+1 x+1 X+ In- +C (x-1)2 (x- 1)2 x + In- X…

A: Given problem:-