z, 1 + 9 + 25 + 49 +81 + ... + /2/

Q: cos e de sin² 0 + 4 sin 0-5

A: To evaluate the given integral.∫cos θ dθsin2 θ+4 sin θ-5

Q: 1. (x+y)dy +(x-y)dx=0

A: Given: (x+y)dy+(x−y)dx=0 ⇒dydx = -x+yx+y   ...(1) To prove: Given differential equation is…

Q: 15. Use the results of problems 12,13 and 14 and assume that the Maclaurin Series expansion for ex…

A:

Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate…

A: We have to find the series is convergent or not and find the sum also.

Q: Find the constant a such that the function is continuous on the entire real line. f(x) = √5x², x ≥ 1…

A: We need to find a.

Q: 1. f(x) = 4x² (8x + 1) 2. f(x) = (100x² + 25x)(10x² − 15x) 3. f(x) = (2x + 1)(4x + 3) (5x - 1)

A: Let's solve all given derivative by using product rule.

Q: Evaluate the integral. (Use C for the constant of integration.) x² - 16 dx +8

A:

Q: Find the area moment of inertia with respect to x of the plane region y=9-x^2 bounded by the…

A:

Q: Solve the following Differential Equations with Laplace Transforms y" - 6y' + 15y = 2 sin(3t), y (0)…

A:

Q: Prove or disprove that the series below converges n-1 Σ(-) n=1

A: Let's prove that given series is converges or not.

Q: Let f(x)= Select the correct description of the one-sided limits of f at x = 0. Choose 1 answer: lim…

A: Above question is solved.

Q: F cos 2x dx sin x

A:

Q: Given the complex numbers z = 2 + j3,zz = -1 - j2,andzg=4+j4 find; Im (高)x+x@zs)+Im(zz+z) (元)

A: solution

Q: Question 4 Find two numbers whose sum is "a", if the product of one by the cube of the other is to…

A: To find out two numbers.

Q: 1 S dx = 3x+2 0-²(3x + 2) + C O 2√3x +2+c 3 O²(3x + 2)² + C A O√3x + 2 + c

A: The given integral is: I=∫13x+2dx  ...1   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: Find the rate of change of the volume (V) of a sphere with respect to its radius (r) when r = 4. 4π…

A: You must have idea about basics of derivatives. The rate of anything is basically the derivative…

Q: Find the derivative: y = ln (3x + 1) O y = O y = Oj = 2 y = = 2ln(3 + 1) (3x + 1) 6 (3x + 1) 3 (3æ +…

A:

Q: TC Find the area of the region bounded by y = cos x, y = 1, and x = =

A:

Q: (2x-1) dx 1 2x²³²-x²-27x +36

A: …

Q: What function do you know from calculus is such that its first derivative is itself? (Do not use the…

A: Here we have to choose the correct option.

Q: 3 A box with a square base and open top must have a volum of 108000 cm³. We wish to find the…

A:

Q: f(x) = 8x7 4 f(x) = X5

A:

Q: Find two numbers whose sum is "a", if the product of one to the square of the other is to be a…

A: sum of two numbers is 'a', the product of one to the square of the other is to be maximum

Q: P3: Calculate the volume of solid of revolution when the region bounded by y = cos x and x² - y - 2…

A: We have to calculate the volume.

Q: Q4) If the power series method was used to solve the following ODE. (x-0.5)y"-y' + (x² - 1) y=0, x=…

A:

Q: TU Find the area of the region bounded by v = cos x. v = 1. and x = ¹₁

A:

Q: So d e2x 0 e2-5 dx is equal to

A:

Q: Taika invested a total of $ (a+b+c+ 900) × 1,000 into three investment accounts, paying 3%,4%, and…

A:

Q: Consider the following. y = = In(x²) Find y'. y' = Find the slope m of the tangent line to the graph…

A:

Q: 2. A certain plutonium isotope decays at a rate proportional to the amount present. Approximately…

A: Let  at time t the amount of plutonium is  A(t)

Q: S (2y-3) dy 2y ³-y²-27y + 36

A:

Q: Using the definition, find the derivative of function 2z-i 1 (z)= at the point z = = -¡. z + 2i

A:

Q: Given f(x) = x² sec x, find f'(x). Ox² cos x + 2x sec x O x² secx tan x + sec(2x²) O 2x sec x tan x…

A: f'(x)=x2secx'         =x2'secx+secx' x2        =2xsecx+secxtanxx2

Q: Question 4 (a) Solve the following: 4x¹dx (b) Explain with the aid of a sketch how this value can be…

A: we have to find the value of integral ∫-22 4x4  dx

Q: 2. Find using implicit differentiation. Enclose final answers. dx (a) 4x³y² + x¹y³ = x + y = 0 (b) x…

A:

Q: (x2+1) з xp x 0

A:

Q: Solve the following Differential Equations with Laplace Transforms y" - 6y' + 15y = 2 sin(3t), y (0)…

A: Let's solve diffrential equation by using laplace transform.

Q: f5(x³ + x)⁹ (3x² + 1)dx O 5(x³+x) ¹0+C 10 (x²³+x) ¹0 10 +C O 45(x³ + x) +C O(x³ + x)¹0+C

A:

Q: Show that the operators T and T₂ from 2 R² into R² de fined by T₁: (F₁) √₂ ) → (9₂9₁) and T2=…

A:

Q: ng expression:

A:

Q: Evaluate lim 00 0-1/1/201 O None of the choices ¹ 0-1/201 O 14 tan z 1 x cos x

A:

Q: 6. Find the symmetric equation of the line parallel to ở = (1,4, 6) + t(−2, 4, 7) that intersects…

A: Given problem:- 6. Find the symmetric equation of the line parallel to r = (1,4,6) + t(−2, 4, 7)…

Q: Q17) Evaluate L (2 e-2t sin4t - 0.5 cos3t): 8 S 8 - a) b) (s+2)2+16 2s2+18 (S-2)2+16 252418 c)…

A: 17) To evaluate: L(2e-2tsin 4t-0.5cos 3t)

Q: TT sinx sin 2x dx 2 cos x

A:

Q: Use the Laplace transform to solve the given initial-value problem. y'' − 4y' + 4y = t,    y(0) =…

A:

Q: 1. f(x) = 4x - 17

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: 30.3. Find and classify the isolated singularities of the following func- tions: +1 Z sin 3z (a).…

A:

Q: Evaluate the indefinite integral du =

A: The solution of the integral is given below:

Q: ſª √√√x – 1 dx is equal to 8 {A}-- 15 32 {B} - 15 - {c} {D} 8 15 32 15

A: To find out the integration.

Q: Find the integration of the following functions COSX 1) dx 3+8sinx 2) fx tan(x² + 1)dx

A: In this question, we want to solve the given integrals.