1. Find an equation for the plane through P,(0,2,–1) perpendicular to n = 3i – 2j-k

Q: 36. a6-72, a13 = 26

A: Student has specifically asked for the answer to the Question-36. Hence, solution to that problem is…

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A: Centroid is x¯,y¯ , where, x¯ = 1A∫ab xfx-gx dx  and y¯ = 1A∫ab 12 fx2-gx2 dxand A = ∫ab f(x)-g(x)…

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Q: Let A = [3 – 2i 4i 1+ 6i], and B = [5+i 2 – 3i 5]. Find (1 - 2i) A + (3 + i) B. %3D

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Q: Determine the area between the functions on the interval [-2, 0]. y = x^2 + 2 and y = 3x + 6 24.67…

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Q: Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3 and…

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Q: H.W: which series converge and which diverge: 1. E 1 1 2. n=1 n=1

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Q: Find the k-component of (curl F) for the following vector field on the plane F=(x+y)i + (8xy)j

A: Solution: F=(x+y)i + (8xy)j       P             Q k-component

Q: 4. If u = (-3, 2), v = (-4, –6), find 4u – 7v %3D

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Q: Find the equation of the family of curves whose slope at any point (x,y) is given and which passes…

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Q: Given k(t)=log_2.4(t+1.6)−3.7 The 3 starting points you would use would be:    . Round answers to 4…

A: Given : K(t) = log2.4(t + 1.6) - 3.7 Basic Function : y = log2.4 t The 3 starting points you would…

Q: Describe the graph of the equation. r = 8 sin 5t i + 8 cos 5t j O Itis a circle of radius 8 in the…

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Q: Write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 4x²,…

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Q: Evaluate the definite integral. (Use symbolic notation and fractions where needed.) dx x2 + 1

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Q: 5. For each integral, state u, du, dv and v you would use to Integrate by parts a) fln(1+x) dx…

A: These integrals are solved integration by parts.

Q: 1 I²+1 Estimate the area under the graph of f(x) = = rectangles and right endpoints. Rn = Repeat the…

A: The Right end point approximation formula is: ∫abf(x)dx=∆xf(x1)+f(x2)+f(x3)+...+f(xn) Divide…

Q: 2. Find the critical points of f(x, y) = x³ + 2y³ – xy and analyze them using the Second Derivative…

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Q: 4. A graph of a function y = f(t) is shown below. Use this graph to answer the following questions…

A: We will use If f(x) is a function. Then roots of f'(x) is called critical points and if f'(a)=0.…

Q: ||r'(t) × x r" (t)|| Use the formula k(t) to find k(t). r(t) = t’i + tl5j %3D K(t) :

A: The given formula is; κt=r't×r''tr't3 And rt=t2i+t15j   As we know that; The Power law; ddxxn=nxn-1

Q: Which of these statements is False? А. (а?)3 — а6 Вв. а?а — а = a' a2 C. a3 = a-1 D. a? + a³ = a°

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Q: The population of a city is 75,000. If the population is declining continuously by 3.7% per year, in…

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Q: Use any method to determine whether the series converges or diverges. √k k³+27 The series diverges.…

A: Given query is to find series converges or diverges.

Q: Let r = xi + yj + zk and r = |rl. r If F = find div(F). (Enter your answer in terms of r and p.) I…

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Q: Calculate the integral. (Use symbolic notation and fractions where needed.) e4x dx %3D - In 2 1 +…

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Q: Verify Green's Theorem by evaluating both integrals aN v? dx + x² dy | dA ду ax for the given path.…

A: Given problem:-

Q: Trigonometric

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Q: |(sin5 (x)) dx

A: Given ∫sin5x dx

Q: The height h, in meters, of an object at time t is given by .h(t) = 12t + 18t 6t² - What is the…

A: topic - functions and derivatives

Q: 6. For each integral, state which trigonometric substitution you would use to integrate by…

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Q: Q9. Which of these is not the derivative of the function, y = x": A. -½x-1½ B. –0.5x-1Vx-1 C. –0.5 1…

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Q: Find the length of the curve parameterized by x = 2 + 3t² and y = 3 + 2t³ from t = 0 to t = 3.

A: To find the length of the curve parameterized by x=2+3t2 and y=3+2t3 from t=0 to t=3.

Q: Find for the equation below. dy dt

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Q: If 3x² + 2x + xy 2 and y(2) -7, find y' (2) by implicit differentiation.

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Q: Consider the curve parameterized by x(t) = 2(t²-1), y(t) = 5e²t, tER Determine an equation of the…

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Q: Vertical and Horizontal area of the plane region y=2x^2+1 and y=x^2+5

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Q: Suppose that f(1, 0, − 1) = 2, and f(x, y, z) is differen- tiable at (1, 0, -1) with Vf (1, 0, -1) =…

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Q: b) c) dx x²(x²-16)2 S S- dx 1 (4x²+3)2 S. X = X = dx = dx =

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Q: the velumg of a Gale ungtrude) finm a agn by Caffing tolume of 54d a Tozt Ximia laca of Card toud…

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A: Given;  limx--2 (4x2+ax+a+12)/(x2+x-2).

Q: lim (- 3" n→+00

A: