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Q: Use the Chain Rule to find dz/dt. z = sqrt 3+ x^2+y^2, x= 3 ln t, y= cos t

A: Use chain rule to differentiate z

Q: Q1) Using numerical integration to estimate the area (r=4 )and c(4,0) with n=4 of the semicircle

A: Trapezoidal rule: One of the most significant integration rules in Calculus is the "Trapezoidal…

Q: Evaluate the integrals for 16 sin²x cos²x dx

A: ∫16sin2xcos2x dx=∫4(4sin2xcos2 x) dx                                 =4∫(2sinxcos x)2 dx…

Q: Find the characteristic polynomial of the matrix, using either a cofactor expansion or the special…

A: topic- matrix operations

Q: Determine whether or not F is a conservative vector field. If it is, find a function f such that F =…

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Q: f(x+h)- f(x) 8x3-4х-2 Problem #1: Using lim, 0 Find the slope of the tangent line y = h Зx+6 at x =…

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Q: A. Plane Area in Rectangular Coordinates Find the area bounded by the given curves. Sketch the…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: What is the absolute maximum value of the function f(x) = x - 3x2 on the interval [-2, 4] ? а. 16 O…

A: This question is based on application of derivative.

Q: For the function shown bellow; Find the second order derivatives : af/ay (a^2 f)/(ay^2) f (x, y) =…

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

Q: Find the distance between points P, and P2. Pi(0, - 3,3), Р,(8, - 4, - 2)

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Q: Differentiate the following. 2r-3 1. y = e

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Q: Evaluate the line integral Vo • dr for the following function p and oriented curve C (a) using a…

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Q: 2 and v2 = -2 3 be -2 Work Problem 2": - - - ;): Let v1 = two vectors in R². (a) '- ; Determine…

A: Given that,v1=2-2 and v2=3-2

Q: Evaluate the integrals in the following questions using integration by parts For 0 cos T0 de

A: By Parts Rule: ∫u(x)v(x) dx=u(x)∫v(x)dx-∫du(x)dx∫v(x)dx

Q: Consider the function f(x) = x2 -1 (a) Find the intercepts of the graph of f (if any). (b) Find the…

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Q: Use sigma notation to write the following Riemann sum. Then evaluate the Riemann sum using a…

A: Solve the following

Q: The demand function for a particular product is given by D(x) = V0.5x² – 2x + 110 dollars, where x…

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Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

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Q: Express the vector 4u + 5w in the form v = v,i+v½j+V3k if u = (3, - 2, 5) and w = (- 4, 5, – 4). 4u…

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Q: L, V4 – x²dx.

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Q: Evaluate, with an exact value, the definite integral º -1/1+a dx.

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Q: J(x+h)-f (x) h 4x+9x+5 Problem #1: Using lim, Find the slope of the tangent line y = 3x-8 at x = -1.

A: Given: y=4x3+9x+53x−8 Let f(x) =y=4x3+9x+53x−8 We know that f'x=limh→0 f(x+h)−f(x)h Now slope of the…

Q: Express cos (a) in terms of cos(2a). Express sin (a) in terms of cos(2a). cos² (a) COS sin (a)

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Q: Sè baucy) dy

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Q: 6. S (1 + 3æ)*dx

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Q: dx The integral of the given function S is equal to (x²–2x+4)ž а. 1/4 b. 1/5 с. 1/6 d. 1/3 e. None…

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Q: O a. X=-9-10A, Y=- 7- 6A, Z= -6-3A O b. X=9+ 10A, Y= 7+ 62, Z= 6+3A P c. X=9-10A, Y= 7- 61, Z= 6-3A…

A: Topic:- geometry

Q: Q/ For the function shown bellow; find dyldx using Chain rule 4 2x + 4)ª ||

A: The function is given by y = 2x+44 To evaluate: The derivative of the function using Chain Rule of…

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

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Q: A local garden store plans to build a large rectangular sign on the interior wall at one end of…

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Q: 12. Find the inverse Laplace: Lª 1 |(s- 4)ª [* et А. e443 В. e44 e43 D. 6 C. E. None 24

A: Inverse Laplace transform shifting property:

Q: Solve the differential equation: y" - 4y' = 0.

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Q: S dx 2x-1 1. Vx+2

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Q: (b) / (4 – t)Vt dt

A: Given integral is definite integral, because here limits are given. In this integral upper limit is…

Q: dz Suppose z is a function of r and y, and csc Vr2 + yz = zesin z. Solve for dz and dy

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Q: 5. y = cot cot (sinx) 6. y = 5 sec sec (2x) + 20

A: We can solve question no 5 and 6 using chain rule as below.

Q: Find the area of the following surface using the given explicit description of the surface. The cone…

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Q: The differential equation (cos(x) sin(x) - xy²) dx + (y - x²y) dy = 0 can be solved by: B. exact…

A: Explained below

Q: 4x + 6 2x2 + 5х + 3 X-1 2х + 4 6. %3D X+ 2

A: According to guidelines, we can answer only one of the multiple questions given. Submit the…

Q: 5. S (16z³ – 14x + 6) dæ

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Q: Give the range of the function f(x) = -x 2. all reals y ≤ 0 y ≥ 0

A: The given function is: f(x)=-x2

Q: 2. Find the Fourier series expansion of: 0, f(x) = -1< x < 0 sin Tx, 0<x <1 and then use it to find…

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Q: Find two sets of polar coordinates for the point for 0 s0 < 2z. (r, 0) = (smaller r-value) (r, 0) =…

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Q: Se*(4 + e*) dx Evaluate the integral of A (4 + e*)² + c B. (4 + e*)? +c (4 + e*)² + c (4 + e*)* + d…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Plane travels for 9.5 hours on two-way trip between location A and B. The Plane can fly at 320 km/h…

A: Plane travels for 9.5 hours on two-way trip between location A and B. The Plane can fly at 320 km/h…

Q: Use the Integral Test to determine vhether the series converges or diverges. ke -8k k=1 Evaluate the…

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Q: Evaluate

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Q: Let i denote the square root of-1. For the two complex numbers z = 3e and w = 6eT find z, w. Give…

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Q: Find the integral of f(3x2 + 4x + 1)*(3x + 2)

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Q: The graph of the derivative y = f'(x) of f(x) is given below. According to the graph, we have f(0) >…

A: We have to tell whether it is true or false