Find a cubic function y=ax³ + bx² +cx+d that has a local maximum value of 3 at -2 and a local minimum value of 0 at 1.

Q: 5: Evaluate I where D is the rigion bounded by xy ve x+y = 7 SS (X+Y) DA D (1

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Q: The area of the region that lies inside the cardioid curve r = cose + 1 and [(cose + 1)² = cos²0]de…

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Q: Evaluate In x x (4 - In² x) - In 14- In² x | +C - 2 In 14-In² x | +C 12 -dx In | x (4- In²x) | +C In…

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Q: Using the given geometric sequence find a7 3,0.3,0.03,0.003 a7____

A: topic- geometric sequence

Q: Given y(t) = e-³tu(t) u(t + 3), where * denotes convolution operation. The value of y(t) as t → ∞o…

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Q: V X if x 3 Find each of the following limits, if they exist. If a limit does not exist, answer…

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Q: (e) If f and g are differentiable then, d -f(g(x)) = f'(g(x))g'(x) dx True False

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Q: Charles plots the point with the polar coordinates (-5,-). How does he plot this point? Drag a value…

A: This question can be solved using the concept of polar coordinates of a point.

Q: Evaluate the integral: 18x² √64 x² - I dx

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Q: Let a = and b = . Find - à - b.

A: Given :a→=5, -5, -1b→=-4, 4, 0

Q: a) yp (t) =) yp (t) = A cos (2t) + B sin(2t) d) y(t) = A cos(t) + B sin(t) Q21) One of the following…

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Q: Given f(x,y)=x2y³-4y, find the directional derivative at the point (2,-1) in the direction of v=.

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Q: If dx = e-²y and y = 0 when x = 5, then the value of x when y = 3 is dx e6 +9 A. e5 C. 2 B. e6 + 1…

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Q: ) a) Find the point at which the given lines intersect: b) Find an equation of the plane that…

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Q: ? Question Draw the gradient f( − 1, 1), starting at ( − 1, 1), on the contour map of f(x, y) = xy.…

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Q: Which of the following statements is true about g(x) = 8 at x = 8? O g(r) is continuous at x = 8 O…

A: Consider the function  g(x)=x+8x-8

Q: a. [CO²2 2 cos²x√4 tan x tan² x da

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Q: t t→0 et (c) lim = 1 True False

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Q: (a) Solve the following: √4x² dx

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: en ủ × ʊ = (2, 3, 4), find (ũ − 4v) × (ũ + 3v).

A: Topic:- vector algebra

Q: Question 4 (a) Solve the following: [²4x¹dx (b) Explain with the aid of a sketch how this value can…

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Q: 3.1 Let f(x) be a differentiable function with f(4)= e and f'(4)=-e. Determine the linear…

A: As per our guideline, we supposed  to answer the only the first question  Given f(4)=e   and…

Q: Given ƒ (t) = L-¹ [³+4 f value of k is 3s+1 s³+4s²+s(k−3) if lim f(t) = 1, then the t->∞0 10

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Q: Find the extreme values of the function f(x)=x√√1- x .- x on the interva

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Q: Find the length of the curve y= 2²-√√x, 4 ≤ x ≤9. 23/2 3

A: To find the length of the given curve.

Q: x(t) = Find a plane containing the point (-3,5,-2) and the line y(t) = z(t) = 5 - 3t 8 + 6t 7 + 6t

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Q: Express the repeating decimal as a fraction. 0.789626262626... 0.789626262626... =

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Q: Find the Jacobian for z = ² + 8uv and y = 6uv². Jacobian (equation format)

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Q: ng expression:

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Q: 20. Stan² x dx

A: Consider the integral  ∫tan2x dx

Q: If f'(x) = 2x³ + 3x² − 4x + 5 and f(0) = 1 and f'(0) = 2 find f.

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Q: Evaluate the iterated integral. "TU 2 √4-22 ²² z sin(x) dy dz dx

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Q: A function g is given. Identify the parent function. Then use the steps for graphing multiple…

A: 10.The given function gx=15x-2.3-7.4

Q: 3) Simplify the expression ' ( ) + (1)

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Q: Determine the value(s) of k for which the following planes will intersect in a lin x+y+z=0 2x + 3y -…

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Q: Question 4 (a) Solve the following: (b) Explain with the aid of a sketch how this value can be…

A: Above question is solved.

Q: How firel the center, foci, vertices and eccentricity for the following equations! x+4y²-4x-8y +4=0…

A: Concept: Ellipse: The equation of the ellipse with center at (h,k)  (x-h)2a2+ (y-k)2b2 =1 Hyperbola:…

Q: If f is continuous and ƒ(5) = 2 and ƒ(4) = 3 then lim ƒ(4x² – 11) = x→2 True False

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Q: 8. Determine if point A(-1, -3, 9) lies on the plane T: 8x-3y+2z=4

A: The point lies on the plane if the coordinates of the point satisfy the equation of the plane.

Q: Determine the first four terms in the binomial expansion of (-3-2x¹).

A: Here we have to open the binomial expansion.

Q: Rewrite the following quantities mo 1) e5ln x+4Lny-In z 2) 2Ln√x + 2Lne - 2Lne*

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Q: * What is inverse Laplace for 1 (s + 1)² + 1 y (s) =

A: option 2

Q: Find the volume of the region of R^3 bounded by the paraboloid z=x^2+y^2 and by the planes…

A: Concept: Let us take D to be a bounded, closed space region. Let a and b represent real numbers,…

Q: Q3) Given, u (x, y) = xy is harmonic, find a harmonic conjugate v(x, y), write u+iv as a function of…

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Q: 3. A 72 N force acting in the direction of vector (2, -1, -2) moves an object from P(3, 4, 2) to…

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Q: 9) Ур H Asin(2t) + Bcos (2t) Q13) The general solution for y' a) = 3x² + c b) = y Q14) The solution…

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Q: x³-y³ Determine whether the function z = g(x, y) = x² + y² (why or why not) for for (x, y) = (0,0)…

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Q: Let ā= . Find a unit vector in the direction of a

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Q: How do i figure out whether this function is continuous or not (proving it) without given at which…

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Q: 6. Find the symmetric equation of the line parallel to ở = (1,4, 6) + t(−2, 4, 7) that intersects…

A: Given problem:- 6. Find the symmetric equation of the line parallel to r = (1,4,6) + t(−2, 4, 7)…