Find the general indefinite integral. (Use C for the constant of integration.) x3 + 12), 343 x*+C 2

Q: Suppose that f(1) = 2, f(4) = 8, f'(1) = 10, f'(4) = -3, and f" is continuous. Find the 4 value of…

A: We have to find the value of the given integral.

Q: 13 4. Consider the function f(x)% = for a 2 (a) Draw a graph of this function on the interval [0,…

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Q: Let (x* + 5)' a Let [(x* +5) x*dx = 12116. Then the value of a is ...

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Q: 3-22 – 47 – 3 dr 2(r² +s + 1)

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Q: Use implicit differentiation to find y′ and then evaluate y′ at ​(3​,10​).   4x3−y2−8=0…

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Q: state whether Converges diverges

A: To state whether the given series converges/diverges. ∑n=1+∞-1nnnsinn1n2n

Q: tan-(n) Consider the series 1+n² n=1 Using integral test, show that the series is convergent

A: The summation of tan-1(n) /(1+n2) ,n from 1 to infinity.

Q: Evaluate the line integral. 17y dx + 16z dy +xdz, r(t) = (2+r',2,P) for 0 <t<1 (Give an exact…

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Q: 2. Evaluate the definite integral. 4 *7 – 7sin²e do 3cos?e

A: I=∫0π47-7sin2θ3 cos2θ dθ1-sin2θ= cos2θI=73∫0π4 1-sin2θcos2θdθI=73 ∫0π41 dθ

Q: Solve the given initial-value problem. xy' + y = e*, y(1) = 8 y(x) = Give the largest interval I…

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Q: Given the power series (x + 4)" n =0 n! Find the "Interval of Convergence" for the series. - 22 - 18…

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Q: CONVERGENT

A: We have to choose the correct option from the given options according to the given information

Q: The h$(2x) sech (2x) dx is equal to sech (2x) sech (2x) +C. A. 1 3 10 B. None of the choices in the…

A: Solve the following

Q: The number N(t) of people in a community who are exposed to a particular advertisement is governed…

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Q: Find the standard form of the equation of the hyperbola with the given characteristics. Vertices:…

A: To find the standard form of the equation of the hyperbola.

Q: Suppose that for a company manufacturing​ calculators, the​ cost, revenue, and profit equations are…

A: Please find all your answers in the conclusion.

Q: n+1 4) Para la serie de potencias (x-2)** halla el intervalo de convergencia. a) (-2,6) b) [-2,6] c)…

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Q: Evaluate the integral / | Vf. dr Vf•dr where f (x,y)=xy² and C is a curve from (1, 1) to (2, 3).

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Q: Evaluate the indefinite integral. (Use symbolic notation and fractions where needed. Use C for the…

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Q: Find the derivatives using Trigonometric Functions 4 y = cos* t – sin* t \1/2 ソ= v = (2 tan² 20 –1)"

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Q: Consider the function f(x)=x^2−4x+1 on the interval [0,4]. Verify that this function satisfies the…

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Q: L Sketch the plane curve by plotting points. Indicate the orientation of the curve. (Hint: Create a…

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Q: Solve the given initial-value problem. dx x = 6y2, x(9) = 1 y - dy x(y) = Give the largest interval…

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Q: Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x - y + z = 2…

A: This question can be solved using the concept of planes in three dimensional geometry.

Q: Activity 1.4.3. For each of the listed functions, determine a formula for the derivative function.…

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Q: A particle moves along the x-axis with velocity given by v(t) = 6t2 – 18 for time t > 0. If the…

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Q: 1. Three students were given the following problem: Unfortunately, we cannot make out the actual…

A: Three students were given the following problem.∫? dx Unfortunately, we cannot make out the actual…

Q: Consider the following function. f(x) = x sin(x), a = 0, n = 4, -0.6 s x S 06 (a) Approximate f by a…

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Q: Find the Laplace transforms of the functions(use limit): a) f(t) = t^2 b) f(t) = t-2e^3t

A: Solve the following

Q: 3 b. Compute the integral S 6x 2 dx using a limit of Riemann sums. Use right endpoints as evaluation…

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Q: e dx (1– e*)2

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Q: In(tan-1x) dx с. 1+ x² 1

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Q: A particle is moving with the given data. Find the position of the particle. a(t) = 2t + 7,    s(0)…

A: This question can be solved using the concept of acceleration, velocity and displacement in terms of…

Q: f(x) dx = | IS(x)| dx =

A: Integration is the area under the curve and x-axis.

Q: dz Use the chain rule to find when %3D and s=2 t=1· - ds z=3x+4y, x=s³r?, _y=s²

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

Q: Set up integrals for both orders of integration. Use the more convenient order to evaluate the…

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Q: Given that z=5cos (3x + 3ct) +e*+. Which ONE of the following statements is TRUE? A. a2z dx2 В. д2:…

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Q: Apply L'Hôpital's Rule to evaluate the following limit. It may be necessary to apply it more than…

A: Solution :let,y=limx→0+cosecxsinxtake log both…

Q: Consider the tollowing Maclaurin series: (-1)"x2" (2n)! CS X = for all x € R. n=0 1. Let f(x) =…

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Q: x²– y² )² Consider the function f (x.y) =| x²+y², Which ONE of the following statements is TRUE? O…

A: We will find limit at (0,0).

Q: Use sigma notation to write the sum. 1 +. +. 9(1) 9(2) 9(3) 9(11) 11 Σ i = 1

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Q: Activity 1.4.2. For each given graph of y = f(x), sketch an approximate graph of its derivative…

A: For each graph of y=f(x) , sketch an approximate graph of its derivative function, y=f'(x).

Q: An evergreen nursery usually sells a certain shrub after 9 years of growth and shaping. The growth…

A: topic - differential equations

Q: Consider an = tan-ln 1. Determine if the sequence {an}=1 converges or diverges. 2. Is the series am…

A: See the answer below

Q: Consider the function g(0) = 3 · cos 2 a. What is the amplitude of g? Preview b. What is the period…

A: This is a problem related to trigonometric function. Based on the general formula we will answer the…

Q: The population of a community is known to increase at a rate proportional to the number of people…

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Q: Convergence of Sequence. For each of the sequences below, enter either diverges if the sequence…

A: Here we have to find whether the given sequence is converges or diverges.

Q: #12: use the definition of the derivative to calculate the derivative of f(x)=9x^2

A: Definition of derivative for a function f(x) is given by f'(x)=limh→0fx+h-fxh

Q: Given f (x,y) =4e** In y with x = In(u cos t) and y = u sin t. The correct value of dz evaluated at…

A: Given fx, y=4e3x ln y, with x=lnu cos t, and y=u sin t.To determine the correct value of ∂z∂u…

Q: 2. A rock thrown upward has a height given by s(1) = 49t-9.81 where s is in meters and / is in…

A: Use derivative to solve