Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (Enter your answers as a comma-separated f(x)=√x, [0, 4] C = Graph the function, the secant line through the endpoints, and the tangent line at (c, f(c)). y y

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A: Using greens theorem

Q: 15. Sketch y = f(x). Properties are: Max at P(2, 2) Mins at Q(4, -1), R(-1,2). Oblique asymptote y =…

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Q: Write the given (total) area as an integral. • The area above the x − axis and below y = 4 − x²

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Q: (D² - 1)y 2 1+ex

A: In this question we have to find the solution of the differential equation.

Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: use the constrained variation to maximize the volume of an open cone when the surface area is 2π

A: use the constrained variation to maximize the volume of an open cone when the surface area is 2π

Q: Determine the sum of the following series. 31 10 Σ(1)

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Q: Susan invested $2,500.00 per year in an IRA each year for 10 years. The interest rate was 7%…

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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: Find the limit. NOTE: Enter the answer using round brackets. t² +7 1 lim t +∞o (?, ?) 5t² + 6'5t,

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Q: (1) What is the approximate volume of a thin cylindrical shell with height 2, radius 3, and…

A: Solution ) Volume of the cylinder    V = πx2h        x = radius         Differentiate with respect…

Q: Verify Green's Theorem by evaluating both integrals ON √ y² dx + x² ov - [/(2x - 2M) da dA R ax ду…

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Q: 01) Solve the differential equation with the given initial condition: y' - 6x²y + 4xy = y. where…

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Q: Evaluate: lim (cos x)=¹2 X x → 0

A: Since the numerator is positive and the denominator x^2 approaches zero and is greater than zero for…

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

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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: 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: Find T(t) and N(t) at the given point. π r(t) = 4 cos(t)i + 4 sin(t)j + tk; t = 2 T (7) 2 ㅠ N(₁) = [

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Q: Use the Root Test to determine the convergence or divergence of the series. (If you need to use ∞o…

A: The detailed solution is given below Thank you

Q: Let G₁ be z = 6-√√36 - x² - y² and G2 be the upper nape of x² + y² - 3z² = 0. If S is the circle…

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Q: Find two positive numbers satisfying the given requirements. The product is 1200 and the sum of the…

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Q: Sketch the region enclosed by the curves and find its area. y = x, y = 3x, y = -x + 4

A: Given; y=x, y=3x, y=-x+4   Now find the point of intersection between the line y=-x+4 & y=3x.…

Q: Is the output true or false, I need the output step by step and a clear line please al = 25 dB al =…

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

Q: Ily approximate the differential dy when x changes from 64 to 64,07 Y

A: Since the student has posted multiple questions and mention to solve question numbers 1 and 2. But…

Q: ergence or divergence of the given series or state that the Root Test is in 1 n=1 non x.)

A: Given :

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

Q: Intervals on Which a Function Is Increasing or Decreasing In Exercises 21-28, find the open…

A: h(x) =x+21/3+8  Or, h'(x) =13x+2-23   We know that,  i) If f'(x) >0 for every x on the interval I…

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A: Find the derivative of 4x3                 Let        y= 4x3

Q: Let R be a plane region with area A whose boundary is a piecewise smooth, simple, closed curve C.…

A: Let's find.

Q: - (lim 11100 ce 1500 = 0)

A: Given limit function :-  f(n) =1500/2n   To check given function is continuous or not

Q: Find the indefinite integral. (Use c for the constant of integration.) [(41³i+ (4t³i + 14tj - 6√tk)…

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Q: Find the limit. Use l'Hospital's Rule where appropriate. If l'Hospital's Rule does not apply,…

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Q: Find the arc length L of the graph of r(t). r(t) = 2 cos(t)i + 2 sin(t)j + tk, 0≤ t ≤ 2π

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Q: p(x), χ b on [a, b], which of the following is/are In f(x) continuous always true?

A: Given that q(x) is  continuous on [ a , b ]  which means f(x) is continuous on [ a , b ] .       as…

Q: Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is…

A: ∑n=1∞  n!22n!

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Q: MY NOTE An open box of maximum volume is to be made from a square piece of material, s = 30 inches…

A: Given: S= 30 inches

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Q: k1 (k+ 1)².4k ak+1 lim ||

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Q: Convert the Cartesian equation Z z = 6-√√36-x² - y² into spherical coordinates.

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

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: F (y)= 2 y-3

A: The given function is  F(y)=2/(y-3).

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Q: HOW ALL WORK pand the logarithmic expression using the properties of logarithms: In xy

A: Topic :- algebra

Q: Which statement is true? If f(x) = 7, then the particular anti-derivative of f(x), is 7x + C If f(x)…

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Q: A table of values of an increasing function fis shown. X 10 14 18 22 26 30 f(x) -11 -5 -2 1 5 Use…

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

A: We know, ddtr1(t).r2(t)=r1(t).dr2(t)dt+r2(t)dr1(t)dtddtr1(t)×r2(t)=r1(t)×dr2(t)dt+dr1(t)dt×r2(t)

Q: Suppose that f(x) and g(x) are given by the power series f(x) = 6+7x+7x² + 4x³ +….. and g(x) =…

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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;…