Q3: Fill in the blanks in the following: A. If u= (1,6,-8) and v=(4,-2, -1) the xu B. The inverse Laplace Transforms [1 1 (s+1)³ C. The angle between vectors A = 1,2,3,4) and B = (0,-1,-4,-2) is. 3s²-s-2

Q: 3 Q19- if z = z =- 4x³y sin sin (x³y) find d əx

A: Given problem:- if z = -4x3y sinsin(x y) find ∂z/∂x

Q: 5. Use the Squeeze Theorem to evaluate lim sin z 2 1-00

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find the area between two curves: 1. Determine the area below f(x) = 8x - 2x2 and above the x-axis.

A: Given: curve y=8x-2x2To Find: Area between the curve and above the x-axis

Q: y = COS X 1+sin x

A: ddxcosx1+sinx

Q: 5. Use the Squeeze Theorem to evaluate lim sinz 42 1-0 6. Find lim f(x) if, for all z > 1, 140 10c²…

A: First i have written the squeeze theorem and find the limiting value of problem (5) and (6) and then…

Q: y' = x y+x²y ) y(0) = −2

A: Here we have to solve the given differential equation

Q: Determine the volume of the region between y=x2 and x=y2 ; revolved about x=1. Show complete…

A: To determine the volume of the region between y=x2 and x=y2; revolved about x=1.

Q: Q.1B) Prove that: Iff, Cos) dxdy - = sin (1) where R the region bounded by x + y = 1, x = 0, y = 0

A: We use the change of variable to prive the given equality

Q: B- The derivative is y = ln (sec (In 0))

A:

Q: Find the surface area of the part of the circular paraboloid z = x² + y² that lies inside the…

A:

Q: A- for the function below, the domain and the range is respectively y = |x|- 2

A: Topic = Functions

Q: Find and simplify the expression if f(x)=x²-11. f(4x)

A:

Q: B) Solve the following 3x -dx (x + 5)(2x - 1)

A: Topic = Integration

Q: Question 5 Newton's law of cooling states that the rate of change of temperature of an object is…

A:

Q: B) Find all of the second derivatives for f(x, y) = (3xy² + 2xy + x²) Ins

A: To find all of the second derivatives for fx, y=3xy2+2xy+x2 ln1x2+y2.

Q: 2- Find the solution of the diff. equ. dy ty Six dx

A: First Order differential equation :        Consider the differential equation…

Q: 4- compute dw dw дх' ду at the point (-2,3) if w = (2x + 3y - 1) ²

A:

Q: ***** EX Estimate the value of 1.1.5 by binamial series. Sol: √1.5 = (1+0.5.) ² X=0.1.5 m = 0.15...…

A:

Q: Q3- Use Green theorem to evaluate [7y-ex]dx+ [15x-sin(y³ + 8y)] dy Where (c) is a positively…

A: This is a application of integral problem

Q: A uniform magnetic field B has constant strength b teslas in the z-direction [i.e., B = (0, 0, b)]…

A: We have to verify that A =12B×r is a vector potential, where r = x,y,0     Given that B = 0,0,b…

Q: Verify that the indicated family of functions is a solution of the given differential equation. A dP…

A: Given  dPdt=P1-P;   P=c1et1+c1etTo Find: We need to verify the solution

Q: B- The derivative is y = ln (sec (In 0)) In 0 sec 0 O it is O it's In 0 cos 0 an O another answer…

A: See the details solution in below

Q: The result of dy/dx for the following function is COS X y = 1+sin x

A:

Q: Use the given transformation to evaluate the integral. J (8x + 8y) dA, where R is the parallelogram…

A:

Q: A- for the function below, the domain and the range is respectively y = |x|-2

A: We know that the domain of a function is the set of input or argument values for which the function…

Q: Please assist with the

A:

Q: give the integral of volume of a solid of revolution when the region bounded by y=x2, y=-2x-1, y=0…

A: This is a problem related to volume generated by solid revolution. Based on the general formula and…

Q: Question1: Classify the following differential equations in terms of the (Type, Order, Linearity and…

A:

Q: C- The result of the following limit is lim 1-0 sin t² t f

A: limt→0sin t2t

Q: 小 7) In x √x - dx

A: I have stated the used formula in the solution

Q: Q2. Let u = (2,-1,1) and v = (3,1,0). Find the following: 1) |2u - v| 2) u ov 3) The angle between u…

A: Given

Q: The coefficient of (x - 1)5 in the Taylor series for a In x centered at x=1 is Hint: you can't do…

A: This question can be solved using the concept of expansion of Taylor series centered at x=c.

Q: WHich of the following represents the shell height if the shell method will be used to find the…

A:

Q: Solve the differential equation: dy y+ = dx

A: Given query is to find the solution of the differential equation.

Q: cos θ =cosθ/csc θ, where θº ≤ θ < 360º, is shown below step one) cosθ=cosθ(1/cosθ) step two)…

A:

Q: dy dx || x3 2+y²

A: Given differential equation, dy/dx= x³/(2+y²) So, (2+y²)dy=x³dx

Q: stion4: Find the general solution for the following second-order ODE as a D-operator form: (D²-3)y=…

A:

Q: Q4) A) Determine the following 1)√√²/1dx 1)ƒ cosxdx 2) S dx 2+3sinx

A:

Q: Use interval notation to write the solution set of the following inequality. x²-3x>0 What is the…

A:

Q: • S/2 csc²2x√√1+cot 2x dx TT/8

A: Given integral , ∫π8π4cosec22x1+cot2xdx

Q: A- for the function below, the domain and the range is respectively y = |x|-2

A: Here we have to find the domain and range of the given function

Q: 3x²y dx − (x³ + y³)dy = 0,_y(1) = −2 -2

A: See the details solution in below

Q: Show the derivation of the following Maxwell relations with complete solutions (F)-(23) Әр as as…

A:

Q: Find the volume of the solid generated when the region enclosed by y = -√√x + 1, y = 0, and x = = 2…

A:

Q: Find the surface area of the part of the circular paraboloid z = x² + y² that lies inside the…

A:

Q: What are the domain, range, and period of the function f(0) = -2cos = -2cos ( - - - 0) + 1₂

A: Let's find domain and range for given  function.

Q: Use the comparison test to decide if the integral converges diverges or if the test is inconclusive

A: Use the comparison test for improper integrals

Q: Find and simplify each of the following for f(x) = 3x - 2. (A) f(x + h) (B) f(x+h)-f(x) f(x+h)-f(x)…

A:

Q: If ū² = and find xu

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

Q: The line whose slope is -3 is tangent to the curve y = x² + 3x + 2 at the point 0 (-3, 2) 0 (3, 2) 0…

A: We will solve the problem.