Find L{f(t)}of the following functions. Note: a, b, e, k and n are constants. f (1) = {'+1,0<1<1 le', t21 1. 2. f(1)=t cos 81 +2

Q: 2. Find and classify all the critical points of f (x, y) = 7x – 8y + 2xy – x² + y³. %3D (1

A: Given: 2.Let us consider the given curve equation, fx,y=7x-8y+2xy-x2+y3 -----1

Q: 2. Evaluate the following integrals (a) / 20° 2x + 3х — 2 dx (b) /: 3x2 + Vx dx (c) / t (Vi – 3t) dt

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Q: 1. Let V = C[-n/2, 7/2] equipped with standard inner product. Show that (sin nr} U {cos mr}1 forms…

A: We will use the basic knowledge of orthogonal sets and vector spaces to answer this question. Basics…

Q: QUESTION 3: Mr. Daily moves to a new province and has the option to either use prepaid electricity…

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Q: [sec 0 tan 0 Ltan 0 sec Find the inverse of sec 0 c. -tan 0 -tan 01 [cos 0 sin 01 Isin 0 cos 0. sec…

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Q: 8. x³y" +x2 y" – 2x y' + 2 y = x³sinx %3D

A: Solution :-

Q: (a) Let V = Rª and let 3 be the standard dot product on V. (i) Calculate B((1,0, 1,0), (0, 1,0, 1)).…

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Q: Check whether the solution is balanced or not. Then, use the Northwest Corner Rule to find the…

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Q: sam deposits 150 in a savings account and earns 6% compounded monthly will she have enough savings…

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Q: Prove whether diverges and state which the following reries converges you or theore test use to…

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Q: Q1. a) Find the Laplace transform of the following expression by using transform tables. f(t) = t +…

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Q: 3. Consider A(r) = (y, -x,0), and the line integral A• dr along the C boundary of the plane x + y +…

A: The given vector function is A(r)=(y,-x,0)., the line integral ∮CA·dr is along the boundary of the…

Q: ifwas T!R3-R² Lineartdentifier T(X gy,Z) =(X +2Y +2g0) grand father ☺ KerT ☺ ImI

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Q: 5. Let o1, 02, 03 be the Pauli spin matrices (? 0 1 1 0 1 03 = 01 02 i and oo = I2. Consider the…

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Q: Numerical Methods a) Employ any suitable numerical methods to estimate the water level from t = 0…

A: A table is given that shows the relation between time and velocity rate while the water is drained…

Q: 3. Calculate the area enclosed by the graphs of y = e* and y = x², the y-axis and the line x =1

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Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

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Q: x +y+ 5z = 0 Solve 2х — у + z %3 0 %D a. (4, 6, –2) b. (-2t, 0, t) c. (-2t, -3t, t)

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Q: Angle between Regression Lines. Suppose one finds the linear regression of y on x and also the…

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Q: From the particular solution of the DE y" + 2y' + y = x at x = 0, y = - 2,  y' = 2, obtain the value…

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Q: A contour map for a function f is shown. 16 of 12 Use the contour map to estimate the sign of the…

A: To find sign of fx , fy we need to check f is increasing or decreasing when we change x by keeping y…

Q: 1 example problem about Area Region Bounded by Different curves. Write the problems and the complete…

A: consider the curves  fx=x2 , gx=8-x2

Q: Solve (x-j2y) + (y-j3x) = 2+ j3

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Q: If g is a differentiable function and g(0)=0 and g'(0) > 0. a) Prove that f(x) = 1/2 (integral from…

A: Introduction: A differentiable function of one real variable is one whose derivative occurs at each…

Q: Let Lin{u} =U, Lin{w} = W, where %3D %3D 3 u = w = Mark only correct statements. O a. The matrix of…

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Q: Identify if the statement below is true or false: The sum of the probabilities in a discrete random…

A: We can solve this by using the definition

Q: Determine a definite integral that represents the area of the region enclosed by r = 7 sin 0 . de…

A: Given:                     r = 7sinθ

Q: Find the constant variation for each combined variation. Then find the value of the unknown quantity…

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Q: Find the Taylor series for f(x) = sin(2x) centered at 7/2. %3D Find the radius and interval of…

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Q: Solve the differential equation Ut Uz(0, t) Uz(2, t) Jo 0<r<1 x 1<x < 2 u(x, 0) You do not have to…

A: Given one dimensional heat equation ∂u∂t=5∂2u∂x2 Given conditions ux0,t=0, ux2,t=0 and ux,0=0…

Q: Test the series for convergence or divergence. Please provide detailed solution. (-1) -1 Σ 5+3n a)…

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Q: f (t) = 7t3 – 0.31t2 + Iạt – cost

A: Given A system that is represented by the given equation ?(?) = 7?3 − 0.31?2 + 8? − cos ?, is able…

Q: III. In a particular very small region, the consumer price index, C, depends on the current value of…

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Q: 1 dx where p> 1 %3D xP

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Q: True or False. Provide reasons a. Let {A„} be an unbounded sequence of positive terms. Then, lim A,…

A: Given: Three statements. We need to check whether the given statements are true or false.

Q: (i) Determine P after 5 years if r = 0.07.

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Q: Show that the determinant gives a group homomorphism det: GL(n,R)->R*, where R*=R-{0} under…

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Q: I. Show that the function f defined by (1, y) = (0,0) %3D f(r, y) (1, y) # (0,0) I+y is not…

A: Given                 f(x,y)=1 , (x,y)=(0,0)                           =x2+yx+y ,…

Q: (b) A system which is represented by the given equation below, is able to work effectively even when…

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Q: х+у+2z %3D0 Solve x - у + z %3D —1 2х + у +z %3D2 by Gaussian elimination. а. (1, -1, -1) b. (1, 1,…

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Q: Find the solution set of x- 4y + 3z = 1. а. (1, 0, 0) b. (-2, 0, 1) с. (1 — 4s + 3t, s, t) d. (1 +…

A: We have to find the solution set of x-4y+3z=1

Q: Consider the following initial value problem: y" + 10y' + 50y = h(t); y(0) = 0, y(0) = 5; %3D S 50,…

A: As per our guidelines, we are supposed to solve only first three subparts. Kindly repost other…

Q: A company produces 4 different types of cookies. a) How many different boxes with 10 cookies is…

A: Follow the steps.

Q: 4 Given matrix A = : 1, find x such that -2 the matrix is singular. а. О с. 3 b. 2 d. 6

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Q: Q2 An electrical device was measured for its current, I fluctuates at a number of different values…

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Q: 3. у") - бу' () - 2у(t) %3 4 сos 2t- 4t3; у (0) — — 2,у'(0) — 3 4 cos 2t - 4t3; У (0) — — 2, у'(0) —…

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Q: Problem 6. rotating D about the line x= -4? important for solving this problem?

A: We will use second theorem of Pappus According to it volume  of a solid generated by the revolving…

Q: The rate of cooling a metal ball can be expressed as dT 3D -k(Т — Та) dt Where T = temperature of…

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Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

A: Consider the given surface, y=x2+z2 Distance of the point 0,c,0 to the surface will be,…

Q: Instruction: Create 1 example problem about Area Region Bounded by Different curves. Write the…

A: Task: We need to create some example problems about the area of the region bounded by different…