Evaluate the integrals: i) ² ²2 xe dy dx **² -xz

Q: Matrix A 3 · 12 21₁B = 1₁ -2] · f find AB

A: Since we are given with multiple number of question and our guideline is solve first question only…

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) ● (esti -j+e-6tk + lime⁹ti…

A: We need to find limit.

Q: The four figures below are graphs of the vector-valued function r(t) = 8 cos ti + 8 sin tj + (t/8)k.…

A:

Q: Sketch the region enclosed by the curves and find its area. Enter the exact answer. Area = y = 5x²,…

A:

Q: If f(x) = 2x-7 and g(x) = x² - 9 then go f= a) 2x - 7 b) (2x-7)²-9 c) 2x²-25 d) none of these 1.a…

A: Finding g(f(x))

Q: Find the partial fraction expansion of the rational expression 2x³ + 3x²2 - 22x - 60 x² x - 12 -

A:

Q: The velocity function (in meters per second) is given for a particle moving along a line. Find the…

A: You must have idea how to find distance under v-t curve.

Q: 3 5. S (t + ²1) ²³ dt t

A: To evaluate the integral.

Q: Consider the differential equation x²y" + xy + y = 0; cos(In(x)), sin(In(x)), (0, ∞). Verify that…

A: Solve couchy Euler differential equation by putting y=x^m

Q: A. ſºf(x)dx = B. If the vertical red shaded area in the graph has area A, estimate: ſ'ƒ(x)dx = (Your…

A: The graph is given as ,

Q: No calculators. Using the Shell method only, find the exact volume created by rotating the region…

A:

Q: Ive the given IVP using Laplace transforms. "-7x'- 8x = 0 x(0) = 1, x'(0) = -3

A:

Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R…

A: Here we have to find the volume.

Q: 13. Consider the functions f(x) and g(x) in the tables below. 5 6 7 8 f(x) 1 4 2 3 (A) g(x)= -f(x)+3…

A: topic- functions

Q: x2/3+ y2/3=4 from x =1 to x = 8. Find the arc length of the curve x²

A:

Q: In (x² + y²) 2 2 VX x+y Integrate f(x,y)== over the region 1 ≤ x² + y² ≤e5.

A:

Q: Solve the following integrals through video presentation. 12x + 6 1. =dx √x² + x

A:

Q: 12. For an object whose velocity in ft/sec is given by v(t) = cos(t), what is its distance, in feet,…

A: Topic = Integration

Q: 1.4 Assuming that C₁ Cos (wot) and C₂ Sin (wot) in 1.2 are two independent solutions of the SHO…

A: It is given that C1 Cos( W0t) and C2 Sin(W0t) are two independent solution of the SHO differential…

Q: 15. Show that the equation, ³ + e* = 0 has exactly one real root.

A: we have x3+ex =0to check number of roots we can draw graph of both and check number of intersection

Q: Solve the given differential equation by undetermined coefficients. y" - 8y' + 20y = 100x² - 65xex…

A: The characteristics equation is  m2-8m+20=0⇒m=4+2i, m=4-2i So, the general solution to the…

Q: Evaluate the integral. Select the correct answer. 6 6 x In (19x) - 12/15 x + C none of these 16 x In…

A:

Q: Set R be the region defined by √2² +²³² ≤4 and let f(z,y) = 1²-22+ y². Find the global maximum and…

A: The region R given is: x2+y2≤4y≥x

Q: 4 Determine -2 u tv and Give a is i and v и So Keat orthogonal to ²-5²³ lutô| = |a²|+12²1…

A: Given the vectors u+v and u-v are orthogonal and  u+v=u+v To find u and v .

Q: Find a bif a= (4, - 1,5) ar . b = (-3, 8, 5).

A: Here we will find whether given vectors are orthogonal or not,

Q: 3. f(2x + 3)² dx

A: I have stated the used formulas in the solution

Q: Find the general isolation of the following: 1. (x³y³+1)dx +x+y²dy=0

A:

Q: Find the indefinite integral. x + 7 √x² + 14x5 Step 1 J To find the indefinite integral dx x + 7 x²…

A: Topic = Integration Fill the blanks with   du = (2x+14) dx

Q: Find r'(t), r(t0), and r'(t0) for the given value of t0. r(t) = (1 + t)i + t3j,    t0 = 1 r'(t0)  =

A: Given the curve r(t)=1+t i+t3 j, t0=1

Q: Integration by Parts; For the following integral, which part would be assigned the u and the dv? S…

A:

Q: Find the derivative of y = ln(x + √√√x² + 1

A:

Q: Find the derivative of F(y). Select the correct answer. F( y) = sinh y tanh y F' (y) = sinh y sech y…

A:

Q: lim 0-4 In[(1 + h)² + 1] - ln(2) y

A:

Q: The resistance R of a copper wire at temperature T = 25 °C is R = 18 22. Estimate the resistance at…

A: Let's solve.

Q: Write v as a linear combination of u and w, if possible, where u- (3, 2) and w(2, -1). (Enter your…

A: Given :- u =(3,2) , w=(2,-1),v=(-6,-4)  Write v as linear combination of u and w

Q: - [² Suppose F(x)= = sin(t) dt. Use the Fundamental of Theorem of Calculus to calculate - (F(x³)).…

A:

Q: Find the points on the graph of the function that are closest to the given point. f(x)=x²-3, (0, -1)…

A:

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) 7x² + 2x…

A:

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. Select the…

A:

Q: The graph of the second derivative f" (x) is given below. On what interval(s) is the function f(x)…

A: Solution

Q: Sketch the plane curve represented by the vector-valued function and give the orientation of the…

A:

Q: a) Sketch the region enclosed by y = x² sin(x) and the x-axis from x = 0 to x = π. b) Find the area…

A:

Q: Problem 7 Proof that if lim f(x) exists then it must be unique i.e., x→a if lim f(x) = L and lim…

A: In this question, we want to prove that if a limit of a function exist then it must be unique.

Q: Evaluate (csc 4x + cot 4x) dx 2

A: Given :∫csc4x+cot4x2dx

Q: The matrix B is the result of performing a single row operation on the matrix A shown below.…

A: Given matrix A=-1374-4-12

Q: The stopping distance for an automobile (after applying the brakes) is approximately F(s) = 1.1s +…

A:

Q: Problem 5 Using Laplace transform, solve y" - 4y + 7y = 0 y(0) = 3, y'(0) = 7

A:

Q: You could take a 15-week, three-credit college course, which requires 10 hours per week of your time…

A: Given :  3 credit college course for 15 weeks. Which requires 10 hours per week

Q: Use Green's Theorem to evaluate the line integral of F= over C which is the boundary of the…

A:

Q: Given r(t)=t2i+5tj, find and completely simplify T(t) and N (t)

A: I am attaching image so that you understand each and every step.