If we apply Rolle's Theorem to the function f(x) = 2x – 12x – 3 on the interval [1, 5], how many values of c exist such that f'(c) = 0? - %3D What is the value of c?

Q: Consider the following. 3D(6,-1,0) v = (-2, 3, 0) u = %3D Find u x v. Determine if uxvis orthogonal…

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Q: Q1: Using the Laplace transforms we found in class, together with linearity, com- pute the following…

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Q: Consider the following. f(x) = 2x - 5 h(x) = x2 - 1 2x - 5 g(x) : x2 - 1 Find f'(x) and h'(x). f'(x)…

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Q: Convert the point (x, y) from Rectangular to polar coordinates (r, 0). 3. (–1, v3)

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Q: 6. For each of the following series determine if the series converges or diverges using the…

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Q: cos(6x2) 22.What should be the value of A so that f A · sin(6x?)dx = + C? %3D 4 A. 3x 4x В. C. 2x D.…

A: ∫A.sin(6x2)dx=-cos(6x2)4+CDifferentiate on both…

Q: Determine whether the following function continuous at point (1, 1). Justify your answer. (x²-xy if…

A: Here we have to determine whether the given function is continuous or not.

Q: A region bounded by f(x) = 5 -x, y 1, and x 1 is shown. What is the volume of the solid formed by…

A: Let's find.

Q: Evaluate the indefinite integral. cos x dx (sin x)27

A: Let's find.

Q: 1.(a) Do there exist integers a, b, c such that gcd(a, b) = 30, gcd(b, c) = 24, gcd(a, c) = 54?…

A: Solving

Q: Use the quadratic formula to solve forx. 5x+5x-1 0 (If there is more than one solution, separate…

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Q: ... * * Find the component form and magnitude of the vector v with the given initial and terminal…

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Q: x2-25 The limit of the function f(x) = as x approaches 5 is equal to -10. 5-x TRUE FALSE

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Q: An integral is given that can be evaluated using integration by parts. Write expressions for u, du,…

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Q: Find the intervals on which f is increasing and decreasing. f(y) = sin y - y cos y on 2' 2

A: Find your answer below

Q: What is the contour map of the function using the given values of k? t(x, y) 1 1 1 1 x² + y? k = 0,…

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Q: A region bounded byf (y) = Vỹ + 1, y = 4, y = 9, and x = 1 is shown. What is the volume of the solid…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: The given parametric curve is: r(t)=cos(πt)i-ln(t)j+t-10k

Q: Determine if the series converges or diverges without using the different tests discussed in Lesson…

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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: First four terms of the sequence n2+3 n 1+8 n are: 4 10 79 28 9 17 75 33 none 4 10 18 28 9. 17 25 33…

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Q: List the first 5 terms of the sequence. 1 22 3n 3n3 32 3n n2 3n (b) -2)n+1 + 3" (a) an =

A: For (a), Given: Now, an=13n3+223n3+323n3+...+n63n3   =13n31+22+32+...+n2   =n+1n+22n+363n3…

Q: Find an equation of the tangent line to the graph of the function at the given point. h(x) = (x² -…

A: Equation of tangent line of a function f(x) at (a,b) is given by, y-b= f'(a)(x-a)

Q: a) f(x)dx = f(x) b) f(x)dx = y = f(x) Area A = 1 Area B = 2 Area C = 2 | 5f(x)dæ = A c) Area D = 0.6…

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Q: The term a,6 of the sequence {an} given by (2 3 4 5'7'9' 11

A: Follow the procedure given below.

Q: Find the area of the region between the graphs of f (x) = 3x3 – x² – 10x and g(x) = -x2 + 2.x, %3D -…

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Q: 2. Determine if the given sequence converges or diverges. If it converges, what is its limit? (a) {…

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Q: 3. For each of the following, state whether the equation is ordinary or partial, linear or…

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Q: Use the formula k(t) : ||r(t) × r"(t|| to find k(t). r(t) = 11 cos(t)i+11 sin(t)j + 6tk K(t) =

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Q: Eliminate* the arbitrary constants c1 and c2 from the relation y = cje-2* + cze³* у" -у — бу %3D 0 O…

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Q: What is the differential equation of the given 1 parameter family of solutions?

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Q: Find the length of curve y In (secx) from x=0 to x=

A: See the answer below

Q: 11. y'+3y = 3x2e-3x %3D

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Q: Find the curve given by x = vt and y =(? – 4), t 2 0 find the slope and concavity at the point (2,…

A: Here, the parametric curve is given by: x=t, y=14t2-4, t≥0

Q: The world population at the beginning of 1990 was 5.3 bilion. Assume that the population continues…

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Q: 4. Given that ! n+1 0.47199 determine the value of " +1

A: Here we have to find the given value.

Q: Find an equation of the plane that passes through the points (-2, 1, 1), (0, 4, 7), and (1,0, –1).…

A: The plane that passes through the point,       -2,1,1, 0,4,7 and 1,0,-1

Q: If P(A or B)=4/5, P(A)=2/3 and P(B)=3/5, then what is the value of P(A and B)? *

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Q: Evaluate the indefinite integral. | x34 sin(x35) dx

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Q: It is determined that the value of a piece of machinery declines exponentially. A machine that was…

A: A machine that was purchased 5 years ago for $66000 is worth $36000 today.

Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(-5, 7,…

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Q: Consider the following differential equation. (x2 + y2)y′ = y2 Let  f(x, y) =  y2/x2 + y2 .  Find…

A: This is a problem of differentiation of the function. Based on the general formula we will answer…

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

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Q: The function f(x) is continuous everywhere. FALSE O TRUE 3.

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Q: Find cos 0, where 0 is the angle shown. Give an exact value, not a decimal approximation. cos e = 17

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Q: Jx + 2x f(x)=- 7х — 4х? 8.

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Q: Compute the following derivatives. Show in at least THREE steps how the chain rule or the outside-…

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Q: The vector v with initial point (0, 0) is shown below. Write v in the form v=ai+bj, where a and b…

A: Given ,  The vector v with initial point (0, 0) We have to write v in the form v = a i + b j where…

Q: 1.(a) Do there exist integers a, b, c such that gcd(a, b) = 30, gcd(b, c) = 24, gcd(a, c) = 54?…

A: (1) gcda,b=30=2×3×5  ...(1)gcdb, c=24=23×3    ...(2)gcda,c=54=2×33     ...(3)

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

A: A detailed solution is given below