Q6) Determine if the following integrals converge or diverge. If the integral converges determine its value. 00 9 dz (1-3z)4

Q: (1) Prove that the product xy of two real numbers x and y is nonnegative if and only if the absolute…

A:

Q: Question (3): Test for exactness and solve the following 1st order linear ODE: (a + 1)y + (b + 1)x…

A:

Q: Confirm that the integral test is applicable and use it to determine whether the series converges.…

A: a)  ∑k=1∞17k+2b) ∑k=1∞11+16k2

Q: 12. A plane 77₂ intersects 7₁: 4x-2y+7z-3-0 at right angles. Two points lie on 77₂: A (3,2,0) and B…

A: Given equation of planes π1 ; 4x-2y+7z-3=0points  A( 3, 2, 0 )  and  B ( 2 , -2 , 1)  lies on  the…

Q: Given F(1) = 2, F'(1) = 5, F(2) = 4, F'(2) = 4 and G(2) = 1, G'(2) = 3, G(4) = 7, G′(4) = 4, find…

A:

Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges.…

A:

Q: Which of the following conditions is NOT required for lim f(x) to exist? x→a

A:

Q: 3 the following first order ordinary differential equatio d. dy = (x²e³x + 6y)dx

A:

Q: Q6) Determine if the following integrals converge or diverge. If the integral converges determine…

A:

Q: Check whether the points (0,7,-10), (1,6,-6) and (4,9,-6) are the vertices of an isosceles triangle.

A:

Q: What is the cartesian form of the complex number: (-1-i√3)4

A: The given complex number: -1-i34.

Q: Quadrilateral MATH is shown. LO 5- 4 -3- 2- M A -5-4-32-10 1 2 3 4 5 -1 T H -5- Quadrilateral MATH…

A: Given data :- M(-1,1) , A(1,1) ,T(2,-2) , H(-4,-3)  Dilation with scale factor of 2.5 Center of…

Q: Compute A B, where A AB= 0 -2 2 -2 0 2 -4 7 8 -5 -1 2 and B = 8 -2 1 -5 -1 3

A: This question can be solved using the concept of multiplication of matrices.

Q: Find the angle between the vectors. (Round your answer to the nearest degree.) a = j + k, b = i +4j…

A:

Q: Given the exponential function f (x) and the logarithmic function g(x), which of the following…

A:

Q: find dt' t= Счи) 11/2 (24)

A: We know that ddxxn=nxn-1

Q: 2x2+3x-2 26x2-x-1 lim x→ 3

A:

Q: If w = cos(xyz), compute for O-x²yz cos(xyz) - x sin(xyz) -x²yz cos(xyz) + x sin(xyz) O x²yz…

A: This question can be solved using the concept of partial derivatives.

Q: (b) Given that s² + 16 (s − 1)(s + 3) (s² + 4) (s Evaluate the values of A, B, C and D. - A B + 1)…

A: We have to do partial fraction of given algebraic expressions.

Q: Solve the given initial-value problem. dx y X= = 4y2, x(6) 1 dy Give the largest interval I over…

A:

Q: Answer 4,5,6

A:

Q: The Great Molasses Flood At 1:00PM on January 15,1919, an unusually warm day, a 90-ft high, 90-ft…

A: We have to solve for force exerted by the molasses.

Q: Find the value of k which makes the following piecewise function continuous for all values of x. k-x…

A:

Q: 12 14 16 18 - 3 9 27 81 ume the first term is a₁ 3 2 20 243 --}

A:

Q: Find the exact length of the curve. y = 9 + ¹ cosh (8x), 0≤x≤7

A: The curve y=9+18cosh8x, 0≤x≤7

Q: Use the root test to determine whether the series converges or diverges. If the test is…

A: In this question, we need to determine whether the given series converges or diverges.

Q: Draw a diagram to illustrate point R divides line PQ such that PR=RQ and R is the midpoint of PQ,…

A: Concept: Vector: A vector is a -dimensional entity with significance and course. A vector may be…

Q: Find the solution of the given initial value problem. y’’+2y’+2y=0,     y(π/4)=2, y’(π/4)=-2…

A:

Q: Use the formula z = ['(t) x r²(c)]. r²(c), Ir'(t) x r"(t)1² r(t) = 9t, to find the torsion of the…

A:

Q: 207 Σ=15 (11). Find sum Σ 15

A:

Q: Find the value of an investment of $10,000 for 12 years at an annual interest rate of 4.55%…

A: Use compounded continuously formula

Q: For y=f(x)=x²-2x+7, find dy and Ay, given x=4 and Ax= -0.2. dy=(Type (Type an integer or a decimal.)

A: Use formula and put value

Q: R: x + 2y = 2, y - x = 1 and 2x + y = 7

A:

Q: A thermometer is taken from an inside room to the outside, where the air temperature is 20° F. After…

A:

Q: Q1. Find the inverse of the following matrix by using Gauss-Jordan eliminations 21 -1 3 12₁ +1 2 120…

A: Given  A= 012-123204 We need to find the inverse of Matrix A using Gauss-Jordan eliminations.

Q: Solve the given initial-value problem. dx y - x = 6y², x(8) = 1 dy x(y) = Give the largest interval…

A: Given problem:- Solve the given initial-value problem.   ydx/dy-x= 6y², x(8) = 1

Q: A. In a moment, you will be providing a system of three linear equations. A private investment club…

A:

Q: If an object is moving along a horizontal line, such that it's velocity, v(t) = = 3¹, what is the…

A: Given :Velocity , V(t)=3t

Q: 5. lim, A.7 Oi O о O. +D T 7x²+x-100 2x²-5x B 712 NIT D.2

A:

Q: Let R be the region bounded by the line y = 1, the parabola y = x², and the curve y = √√. Find the…

A:

Q: Solve the given initial-value problem. y x = 6y², x(8) = 1 dy x(y) = Give the largest interval I…

A: To solve the initial value problem.

Q: R. H. side is 3 2 [ f z=1 y=1 -2(x+1)y dy dz

A:

Q: You want to build a 1100 square foot rectangular infinity pool. Three of the sides will have regular…

A:

Q: -2 2 /y + 2 dy + √ ² [√y+2_y] dy

A:

Q: 2-x x+²√√x+2-√√3x-2 c) lim-

A:

Q: FOR NUMBERS 8-10 8. Evaluate (x) = 5x-1 A 1 9. f(x)= 3x² A 3 10. f(x)=-4 A 3 (2) for the given…

A: Topic = Deriative 8) B 9) D 10) C

Q: Find the derivative of f(x) = 2x3 + 12x² +18x + 9. f'(x) =

A: To Find : Derivative of f(x)=2x3+12x2+18x+9     Note that : Derivative of xn is nxn-1

Q: y' = X y+x²y , y(0) = -2

A: Given differential equation: y'=xy+x2y, y0=-2To Find: solution of the differential equation

Q: Consider the region S shown in the figure below and take note of the following points of…

A:

Q: Exercise 1.8. Prove (1+2+...+n)² = (1+2+...+ (n − 1))² + n³ by mathematical induction, and discuss…

A: