Find the range for the function x²+y²=4

Q: 17. Let y = 4t² + 3, t = 6es and s = 1 + In x. Find in terms of x. dx 18. Given y = 5t (3 - t), t =…

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Q: Find the area of the region enclosed by the parametric equation x = t³ - 7t y = 6t²

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Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for…

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Q: Express the series using sigma notation 5-10 + 20-40+80 °5(-2)-¹ 21 -2n-5 7-1 0-5(-2)-1 -2(5)-¹ 7-1…

A: Infinite series

Q: Given a sin 6t and y = cos 6t, find the following derivatives as functions of t. dy/da 1 d'y/dx² =

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Q: equation and the initial condition. 8. f'(x) = 9x² + 1, f(0) = 7

A: Given problem:- Solve  f'(x) = 9x² + 1, f(0) = 7

Q: Given: xy =tan(x - y). Find dx/dy. tan² (z-y) soc²(z-v) +tan² (z y) sec (x−y) -sec² (2-y)-z 當…

A: find derivative dxdy from equation xy=tanx-y

Q: Express the limit as a definite integral on the given interval. n lim [7(x)³ - 5x;*]4x, [2,7] n→∞ =…

A: Here, the limit of the integral is [2, 7]. Further, ∆x is replaced by dx and replace xi* by x. Thus,…

Q: F. dr if Using any method, find the value of So F(x, y) = (6e + 3ye") i + (3eª + 6xe²) j and πt C:…

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Q: Find the limit. NOTE: Enter the answer using round brackets. t² +1 1 lim t +∞ (?, ?) 6t² + 7' 3t ||

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Q: For the given vectors a and b, find the cross product a × b. a = (1, 0, -3), b =(3, 4, 0) axb=

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Q: A particle is moving with the given data. Find the position of the particle. a(t) = 2t + 9, S(0) =…

A: In this question we have to find the value of s(t).

Q: Find f. f(x) = f''(x) - 10 + 6x + 24x², f(0) = 5, f(1) = 16

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Q: Solve for the solution of: (D3 + D)2y = 0

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Q: 10. Given that y = at x = 1. e* X + 1 Find, in terms of e, the values of . 최 and dx dx²

A: (10). Given: y=exx+1   As we know that; The Power law; ddxxn=nxn-1 The Quotient rule;…

Q: Homework 11 Parametric: Problem 5 Given ze and y = tet, find the following derivatives as functions…

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Q: Question 3 Select all of the following tables which represent y as a function of a. I Y I x y I y…

A: Let's find.

Q: Solve for the solution of: (D2 - 4)y = 8e2x - 12

A: Given problem:- Solve for the solution of: (D2 - 4)y = 8e2x - 12

Q: Evaluate F. dr along the curve C if F(x, y) = (x² + y²)¯³ (xi+yj), с and C: r(t) = et sin ti + et…

A: F.dr is integrated along the curve C.

Q: Introduction to Derivatives ections: Read the paragraph. On a separate sheet of paper, answer the…

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Q: Solve y"+y' + y = 6sin (2x) supo

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Q: The smaller the curvature in the bend of a road, the faster a car can travel. Assume that the…

A: Given that the smaller the curvature in the bend of a road, the faster a car can travel.

Q: d [r₁(t) · r2(t)] = [r₁(t) × r₂(t)] : = d

A: Given: r1t=costi+sintj+8tkr2t=7i+tk

Q: d d Calculate[ri(t) r2(t)] and [r₁(t) × r₂(t)] first by differentiating dt dt the product directly…

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Q: Evaluate the definite integral. NOTE: Enter the exact answer. |ti + t²j||dt

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: Solve the differential equation: (D41)y = 0

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Q: Evaluate the definite integral. 15t L² (elst i + e i+e¹j+t k dt 1 k)di

A: Here we have to use the concept of definite integral.

Q: Evaluate the vector-vall function at each giver r(t) = cos(t)i + 3 sin(t)j (a) r(0) = (b) г(π/4)=…

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Q: Determine whether F(x, y) = 6x²y i+ 4xy²j is a conservative vector field. If so, find a potential…

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Q: The differential equation regarding the family of curve y = e 500x 1S

A: This question is based on diffrential equation.

Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

A: Evualate the vector valued function

Q: Let f(x)=(x-3)-2. Find all values of c in (2, 5) such that f(5) f(2)= f'(c)(5-2). (Enter your…

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Q: Problem 3

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Q: Find the integral of the following equation integrate cos(x + pi/3) dx

A: Given problem:- Find the integral of the following equation integrate cos(x + pi/3) dx

Q: Find two positive numbers that satisfy the given requirements. The sum of the first number squared…

A: Let, the first number x and second number y. Given that the sum of first number squared ( x2 )  and…

Q: Use the following binomial series formula to obtain the MacLaurin series for ∞ (a) (1+z) k=0 (b) √ 1…

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Q: If f(3) = 11 and f '(x) ≥ 3 for 3 ≤ x ≤ 7, how small can f(7) possibly be?

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Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

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Q: 518 SHOW ALL WORK Aau aາq JV Find the exponential function given by f(x) = Ca that models the data…

A: f(x)=Caxf(0)=Ca02=CC=2Thereforef(x)=2axf(1)=2a16=2aa=3Thereforef(x)=2×3xCheck for x=2 and…

Q: Find the limit. lim 1→2(t i - 5 j + t² k)

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Q: d d Calculate[ri(t) r2(t)] and[ri(t) r2(t)] first by differentiating dt the product directly and…

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Q: Using the Mean Value Theorem In Exercises 13-18, determine whether the Mean Value Theorem can be…

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Q: Finding an Indefinite Integral In Exercises 1-6, find the indefinite integral. 6. ·S(10² + x³/2) dx

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Q: Finding the Volume of a Solid In Exercises 23-25, use the disk method to find the volume of the…

A: We have to find the volume by disk method.

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

A: Using greens theorem

Q: Homework 11 Parametric: Problem 3 Suppose a curve is traced by the parametric equations as t runs…

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Q: Use the form of the definition of the integral given in this theorem to evaluate the integral. [²4x³…

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Q: 03) Prove or disprove that y = ce* + de ²x is the solution to y(2) + y(¹) - 2y = 0.

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Q: A 10,000 litre rainwater tank is to be built in the shape of a cylinder. It must be at most 3 metres…

A: As per our guidelines we can answer only 3 subparts of the given equation. Kindly repost the…