9. Show that if n is a positive integer then n Σ k² ( x ) = n(n + 1)2²−² k k=0

Q: Find the derivative of the parametrically defined curve (t) = 2 cos(4t), y(t) = sin(4t). dz 4cos4t…

A:

Q: Which of the following is the formula for the length of the arc, L, of the curve y = f(x) such that…

A: The answer is given below:

Q: General solution of dy dx = tan²(x + y) dx

A: This question can be solved by taking x+y=t

Q: For questions no. 4 and 5. Given: Radium decomposed at a rate proportional to the quality of radium…

A:

Q: 2. Simple Chemical Conversion Radium decomposed at a rate proportional to the quality of radium…

A: This is a problem related to decay law. Based on the general formula and concept we will answer the…

Q: Given [ƒ(x) a f(x) dx = -5, and g(x)={3x+2,355 / 3x+2,3≤x≤5 integral. Find the value of k that…

A:

Q: PRACTICE Q7. Consider the series Σ(−1)n-1 (x + 1)" n-0 nb2n where b is a given non-zero constant.…

A:

Q: 2. The Minimum point of y= 320

A:

Q: Numerical Integration: •2 1 [.. -dx Jo √x 1.

A: Numerical integration

Q: y = x² - 6x² + 8x and y = x² - 4x. 2. Find the area bounded by the two curves y:

A:

Q: y"+y=2xsinx

A:

Q: General solution of = dx tan²(x + y)

A:

Q: The graph of a rational function, f(x), has a point of discontinuity when x = 2 and an asymptote…

A:

Q: it was estimated that constructing a fence for a project could be done by 11 workers in 15 days. at…

A: Let 'n' be the number of workers. Let 'd' be the number of days required Let WT be the work done…

Q: Q2/ Find the first moment about y-axis of the region in the first quadrant bounded by the x-axis,…

A:

Q: Find the domain of R. R(t) In(1 t) √t+1, e-¹/|t| {(VEFT, 0-10m, bu(1-2)}) t = (1,0,-1) " , if t #0…

A:

Q: 8. 位 dx √x

A:

Q: The equation of the line containing the points (5,6) and (3,4). y=x-140 y=x+2.80 y=x-2.00 y=x+1DO

A: Topic:- application of geometry  And equation of straight line

Q: II. Solve the following problems. Enclose final answer. 9. A gutter with trapezoidal cross section…

A:

Q: (j) [e³ sin 2rdr

A:

Q: for a system of two equations in two variables, the graph of the equations are the same lines, then…

A: We have to find out the solution existence

Q: The value of f (3), for the following function f (x)=√√2x-20

A:

Q: 32 Remove parentheses and simplify: [4(x + 3) - 4x] -4(x + 3) 4x A O -2x BO 2co -4x-Da

A: Let's simplify.

Q: 1. 2. dx dx sin²(x² + 2x + 1) [4 tan(3x³) - 5 csc x]

A: To find derivatives

Q: ƒ(z) = (z³ + z − 4); [−1,2] x h(x) ; [0,2] x-3'

A: Mean Value Theorem:  f'(c) = (f(b)-f(a))/(b-a)

Q: A. Determine whether each integral is improper. If it is improper, give your justification. dx 2.

A:

Q: Find the values of p for which each integral converges. 2 80 dx dx b. x(In x)P x(In x)P GELEH 2 dx…

A:

Q: 8. The general solution of y"- y = x²ex + 5

A:

Q: 11. In each part state the x-coordinates of the inflection points of f. Give reasons for your…

A: We want to find inflection points.

Q: Find the limit. x² - 25 lim x 5 x²8x + 15

A: We need to find the limit:limx→5x2-25x2-8x+25

Q: The lines y = - 2 and x = 2 are perpendicular. صواب خطأ

A: We have to find out solution

Q: 4. Consider the sequence {n} (a) Write out the first five terms of the sequence (b) Determine…

A:

Q: Numerical Integration: S 0 7. =dx X

A: We want to find value of integral.

Q: B. Determine whether the following definite integrals converge or diverge and evaluate each…

A: Given problem:- Determine whether the following definite integrals converge or diverge and evaluate…

Q: Find x, y and z, if the matrix A = a) x= 2₁ y= V₁ = √3 b) √√6 =√², y = x= 2= c) None of these d)…

A:

Q: We are interested in the first few Taylor Polynomials for the function f(x)= 7e + 3e-* centered at a…

A:

Q: Consider this function: f(x) = 2x³ +5x² - 4x - 3 This problem has four parts. Be sure to answer all…

A:

Q: The region bounded by y = 3x - 9 andy = -3x2 + 18 x - 9 revolved about the y-axis. Find the volume…

A:

Q: The value of the exponential form is the subscript in the logarithmic form. (A) True B) False

A: As per guidelines we can answer only one question at a time so if you need more answer kindly repost…

Q: 3. Using the Gauss-Seidel method make three iterations for the linear svstem x(0) = 0, 4x - y -z =…

A:

Q: Find the length of the arc of the curve y = (1 + x²) fron the point where x = 0 to the point where x…

A:

Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t)= -…

A: Given query is to find the height when velocity is 100ft/sec.

Q: Q9. The Laplace transform of the function u: [0, ∞o) → R (t−2)² + (t− 2) sin(5(t-2)), u(t): can be…

A:

Q: Compute the partial derivative of the function * with respect to z at the point (1,0, 7). Compute…

A:

Q: So .x² dx (2x²+2x+1)²

A:

Q: 3. The Critical Point of y=xe*

A:

Q: 5. The auxiliary equation of the differential equation (4D³ - 13D + 6)y = 0 falls under_ Prove your…

A:

Q: The Intermediate Value Theorem can be used to prove that the equation z² - 5x+6=0 has at least one…

A: Given :x2-5x+6=0

Q: 8. A street light hangs 24 ft. above the sidewalk. If a man 6 ft. tall walks away from the light at…

A: We can find the required as answer as below.

Q: Calculate the points of intersection of the curves x² = 4y and bre yavas r3 099wied biloa 9d1 to 9…

A: