INSTRUCTIONS: (1) Answer all questions neatly with a blue or black ball point pen/ink pen. (2) Use A4 size white paper to answer the questions. Q1. Find the area of the region enclosed by the two curves, y = 2x² + 3x and y = x² + 5x

Q: 36. Which one of the following is true for all z ER? (a) z sin(2) dx = (1-2) cos(x) + C (c) (b)…

A: Now that we know that the integral of x sin x is equal to −x cos x + sin x + C, we will derive this…

Q: Question 3 (a) (b) Show that the solution y(t) of the initial value problem has the Laplace…

A: This question is all about laplace transform.  We know that laplace transforms are as  L{y"} =…

Q: Determine if +∞o 5 dx √x-1 is convergent or divergent.

A: Solve the improper integral then using expansion at infinity solve limit

Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

A: Given problem:- Find the absolute extrema if they exist, as well as all values of x where they…

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: Use synthetic division to find the function values. Then check your work using a graphing…

A: Use synthetic division to find the function values  f(x) = 3x5-4x4+3x3-3x+8 , find  f(18) and f(-3)

Q: Draw a direction field for the differential equation y'= -y(3-y). Based on the direction field,…

A: Given

Q: 1. (2xy² + 2y) dx + (2x²y + 2x) dy = 0, 2. + 6x) dx + (In x - 2) dy = 0, x y(1) = 3 y(e) = 1

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Q: A) e-2 Β) e2 Σε e=2n =? 71=0 C) CADEMI Ε)

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Q: The population of a town grows at a rate proportional to the population present at time t. The…

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Q: a. S ((e'+4)²-9)3/2 -dt

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

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Q: For the next two exercises, determi Hiverges. 3 Ž. Σ (-1)" √n + √√√n+1 n=1

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Q: 5 Qu/ If w=f(u, v) = cos uv, u = xyz , v = 4(x²+y²) dw Prove that 0 at the this point…

A: Given problem:-

Q: Find the second derivative of the function. f(x) = 5(2 − 7x)ª

A: Given query is to find the second derivative.

Q: Determine the slope of the tangent line to the curve of intersection of the surface f(x, y) x + 2y x…

A: According to the guidelines, we are answering first question. Please repost the remaining.…

Q: 8. Determine the area bounded by x = -y² + 4y and the y-axis.

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Q: x TC Q2\ Find The Area under the curve Y= 4sine between X= and 2 X= π by the double integral method.…

A: Let's find area by using double integral method. Small mistake in given question, there should by…

Q: Let u = cos(4x) and du = e² da, then by using IBP, the integral [e²= cos(4x) e2x cos(4x) dx is equal…

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Q: Matrices A and B below are row equivalent. For each of the concepts following, choose (check) one…

A: See the answer below

Q: 2 Σ(-1)+1n? + 5 m2 + 4 n=1

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Q: Q3: A) Prove that eie = ei(0+2x),where k = 0,±1, +2,.....

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Q: 9. The value of q will make the roots of quadratic equation 9x²-4qx+4=0 be equal are A.0 B. q-3,-3…

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Q: Find the indefinite integral. (Use c for the constant of integration.) [(20 (2ti + j + 6k) dt

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Q: b. |ā + (bx c)|

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Q: f(x) = ln(x − 1) at x = 2

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Q: Find when y = cos(sin 2x). ay dx dy dx

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Q: Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify…

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Q: x²-3x-10 x 5 x²-8x+15 9. lim

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Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y=2rsinė

A: this is a problem of differential. Based on the general formula and concepts we will answer the…

Q: 6. lim x-3 x2+4x+3 x+3

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Q: x²-100 4. lim x-10 x+10

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

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Q: 10. Show that these two lines are coincident. [x, y, z]= [1, 5, -2]+s[1, 7, -3] [x, y, z]=[-3, -23,…

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Q: Find the integration by using Partial fraction method x² + 2x + 1 (x² + 1)² dx

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Q: Q3/ Evaluate: ff(x+y) dy dx for the region bounded by the x = 0, x = 2, y = x and y = x + 2

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Q: Evaluate the following integral. r/4 1 (s secx- cos cos sx)²dx 0 x/4 ļ (secx- cos x)²dx= 5 3 4 8 0…

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Q: Find 3rd derivative if ƒ'(x) = x³.

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Q: Which of the following gives the volume of the solid obtained by rotating the region bounded by y =…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Q2/Examine the following surface for maximum, minimum, and saddle points z = x² + y² + xy + 4x - 4y…

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Q: 2 - 772 + 317 - + ه ها- لا + 772 - 222 . 2x 3

A: Concept: Without upper and bottom constraints, indefinite integrals are defined. It's stated like…

Q: hand-tossed pizza base starts off as a ball of dough with a volume of 400π cm3 . First, the cook…

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Q: Given the following piecewise function, evaluate lim f(x). x→2 -x² - 2x - 2x² - 1 f(x) = -2x² - 3x +…

A: Explanation of the answer is as follows

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

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Q: 7. Determine the area bounded by y = x² - 6x + 10, x = 1, x = 5 and the x-axis.

A: Above question is solved.

Q: 6 5 4 1 -7-6-5-4-3-2-1, 1 2 3 4 5 6 7 -3. -6 147

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Q: An open box is to be made from a square piece of cardboard of side 12 inches by cutting out squares…

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Q: Name the quadrant in which the angle 0 lies sin 0>0, cos 0 >0 The angle 0 lies in which quadrant?

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Q: Use implicit differentiation to find d²y = dx² d²y dx² if 8y+sin y = x.

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Q: 15. Given: Th: x+y+z=0 Find: the value of 'm T₂: x+2y+2z-1=0 That a line that lies on the plane 773:…

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