Let f(r) = r³ – 3x² + 4. Using the Mean Value Theorem, determine the value of c € (0, 3) such that the tangent line to the graph of f at the point where r = c is horizontal.

Q: 1. Solve the following quadratic equation by completing the square: x2 – 6x +4 = 0

A: We are authorized to answer one question at a time , since you have not mentioned which question you…

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A: Given

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Q: C. VARIATION OF PARAMETERS 1. (D² + 1)y = secx tanx 2. (D2 – 3D + 2)y = 1 1+e-x

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A: We have to determine the given series is converges or diverges

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A: Let's find.

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Q: V9x2-12x +11 Evaluate lim x-1/3 3.x-1 -2 O NONE OF THESE O O o O O

A: To evaluate the following limit.limx→-13-9x2-12x+113x-1

Q: Consider the following. u = 3i - j - k, v = -i + 5j + 7k %3D (a) Find the projection of u onto v.…

A: Given :  u=3i-j-kv=-i+5j+7k   To Find: a)Projection of u onto vb)Vector Component of u orthogonal to…

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A: To find equation of line passing through the point 2,6,−1 and perpendicular to both vectors −4,3,−5…

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Q: Composition. Suppose we want to find the composition of a function with itself. Let g(x) = -3(x+5)2…

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Q: 2. t23* dt

A: The given problem is solved below in detail.

Q: Consider the following equation and point. f(x) = a (3, -1) x - 4 Find an equation of the tangent…

A: First we have to calculate slope of the given function to calculate equation of tangent

Q: Evaluate the solution of differential equation when y(0)=1 and y'(0)=D0. d?y dy-8y 0 %3D dt? dt

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Q: Find the following. = (3, 5) U = %3D (a) ||u|| (b) ||v|| (c) ||u + v||

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Q: 3. Is the function f(x) = csc2 + sec x- cosr even, odd, or neither? Show algebraically. %3D 4. Write…

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Q: 6. Change the order of integration and evaluate the integral y+1 у? dxdy -1 Vy+1

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Q: 33 f(x) = sin 2x + Ve2x + 2x – In e, x # 1 1-x

A: derivative

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Q: y ~ y=x+1 x=4 y=0

A: Given: Now find the x-intercept of the line y=x+1. y=x+10=x+1x=-1x,y=-1,0 Now taking an elementary…

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Q: 1. If f(x)=1/x, which of the following is the simplified form of the difference quotient? * -h -1…

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Q: A. Given: lim f(x)=-9 lim g(x)= 2 2. lim[3h(x)–6] 4. lim[f(x)- g(x)+ h(x}] lim h(x)=4 x→8 x→8 x→8 1.…

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Q: Find the following. u = (0, 1), v = (5, -3) (a) |u|| (b) ||v|| (c) |u + v|| (d) |u| M (e) U + V (f)…

A: We can solve this as follows:

Q: Find u · v, u · u, ||v||². (u - v)v, and u · (3v). u = (3, 12), v = (-2, 3) (a) u. v (b) u.u (c)…

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A: Let's find.

Q: 1) Find the second derivative of y = csc 2 e cot 2e %3D

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Q: (-1) Investigar la convergencia o divergencia de la serie E1 n+2

A: answer is in next step

Q: 5. St V1-t dt

A: We solve this integration by substitution method by putting                         1 - t3 = u…

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Q: Eliminate B and a from the relation. x = B cos(mt + a) *+ 2wx = 0 O * + w?x = 0

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Q: Consider the following. u = 6i – j - k, v = -i + 5j + 3k (a) Find the projection of u onto v. 2i 17j…

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Q: Question Evaluate the following limit using L'Hospital's rule. 168 2.x lim X12 [5x2 - 85x + 300…

A: topic - limits

Q: 1. If x = cos t and y = sin? t, then dy/dx is 2. Find Zxyx if z = xe?y + ye2x. 3. If s 10 t? + 80/t,…

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Q: Question Consider a continuous function f(x). The function has critical points at.x = -2, x = 2, and…

A: topic - application of derivatives

Q: Find the derivative of the function described. (Rx5) 4х-2 5. у 3 3x+4

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Q: 1 у 3 2 y (х + 2)

A: y = (x+2)-1/2 dy/dx = (-1/2)(x+2)(-1/2 - 1) dy/dx = (-1/2)(x+2)(-3/2) dy/dx = -1/2(x+2)3/2

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A: As per the guidelines I am supposed to do the first question among multiple questions. So I am doing…

Q: Find the derivative of the function described. (Rx5) 3x-1 2. f (x) = 2x+4

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