Evaluate the following antiderivatives. S 4x dx 4e e8x +4

Q: Find the area bounded by r = cos 0 for -π/2 ≤ 0≤π/2. 2. Find the length of the r(t)= , 1 ≤t≤ 5 .…

A: We have to solve Questions 12.

Q: Find the sum of the values of f(x) = x³ over the integers 1, 2, 3, ..., 10.

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Q: Solve the following initial value problem completely, and check your answer by comparing it to the…

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Q: p(x) Given the Rational Function f(x) = q(x) Assume the numerator and denominator have no common…

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Q: Let f be a function with continuous second partial derivatives and define: z = f (2x³y - y₁y³) if…

A: z= f(2x3y-y,y5) ,  u= 2x3y-y, w= y5   And zy= (2x3-1)fu+5y4fw  Find zyx

Q: 2) By using Lagrange multiplier method, find the maximum value of f(x, y, z)=x+ z subject to the…

A: Given function:-     f(x, y, z) = x + z subject to condition x2 + y2 + z2 = 10

Q: Use differentials to estimate the amount of paint needed (in m3) to apply a coat of paint 0.04 cm…

A: Our Aim is to find the amount of paint required to coat thickness of 0.04 cmby considering a…

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by…

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Q: sec² x 0 1+tanx If sh -TT/2 -TT/4 TT/3 TT/6 O dx In 2, then what is the value of k? =

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Q: Let P be the set of points that belong to the shaded region imaginary The set P is (A) open (B)…

A: We can see that the outer boundary is not included in the region. So set is not closed.  We can see…

Q: Using the Inverse Function Theorem, what is (-1) (8) given that /(x)=√6x-2? Note that (11) = 8. (Do…

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Q: 11. Find the position r(t) of an object if the acceleration is a(t) = and the initial position is…

A: We have to find out r vector

Q: (7) ² Fi²+ Fi²+ ² Fi Fz Cos/20 49=F₁²+ F²-FiFe- tan 8= 48- = 4√3 4√3= F₂S in 190 Fit F₂ Golze $7…

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Q: I(X) {(-2,1), (1,4), (2,5), (3,6) g(x) = 6 + 4x h(x) = -x² + 2 2. 2h(3)+g[f(-2)] find 1. h[f(1)] 7…

A: 1. hf17=h47                  =-16+27                   =-147                    =-22.…

Q: Q1A)The vectors A = 3i+j+ 4k, B= 2i-3j-k, find vector normal to A and In plane of A and, B.…

A: Let's call the vector to be found is C. C vector will be normal to both vector and A and B. we can…

Q: xp (x+)ɔ zx f

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Q: The right-endpoint approximation of the area under the curve of f(x) = x² over the interval [0, 2]…

A: fx=x2 over the interval 0,2 for n=4

Q: sint do соби Ө

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Q: Question 7 Find the partial derivative of z with respect to x 8: da = -2x (3x²+1) sin(x²) + 6xcos…

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Q: The position function of a particle is given by the equation s(t) = -2t2 + 3t + 10. Determine the…

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Q: A region bounded by f(x) 6 5 4 3 Find the volume of the solid formed by revolving the region about…

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Q: If [ f(x) dx O 10 0 2 O O -2 = 4 and 4 [*g(x)dx = 6, what is 5 2 [ f(x)dx + ² g(x)dx? 4

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Q: Solve the differential equation: dx dy + x = e-y.sec²y

A: Here we have to solve the differential equation.

Q: 16. Integral Ydy 6y2-1

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Q: B)Is w = Zez analytical function or not?

A: In this question, we want to know whether the given function is analytic or not.

Q: 59. x² + 2x + 4y - 3 = 0

A: Here we have to find the vertex and focus of parabola.

Q: Given the functions: f(x)=x²³-8x g(x) = √2x h(x) = 6x+7 Evaluate the function h (f(x)) for x = 3.…

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Q: Find the equation of the tangent to the curve at the point where x = 1. f(x) = √x 2√x+1

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Q: Find dy/dx by implicit differentiation. 19) x3 + y3 = 5 20) 2xy-y2=1

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Q: Write an equation for a rational function with: Vertical asymptotes at x = 3 and x = -4 x intercepts…

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Q: Given f(x) = 3-5x³, use a table to estimate the slope of the tangent line to f at the point P(0, 3).…

A: According to question,Given Function,fx = 3-5x3P0, 3Qx, fx

Q: Find a vector-valued function, using the given parameter, to represent the intersection of the…

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Q: in winding up the cable when there is a 400-pound load attached to the end of the cable. ft-lb

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Q: 13. Find the distance from the point (2, 2, 3) to the plane 2x+y + 2z = 4.

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Q: Find the area of the region enclosed by the graphs of the polar curves given by 8/4, 0 = 0 and r cos…

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Q: A baseball is hit 3 feet above the ground at 80 feet per second and at an angle of 45° with respect…

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Q: Classroom activity 9.1 the monthly income earned by each of the following workers paid by the hour…

A: We have to determine the monthly income.

Q: The graph of the function f on the interval [-4, 4] is shown above. What is the value of f(x)| dx? 5…

A: integration

Q: A particle is moving along the x-axis so that its velocity at any time t≥ 0 is given by v(t) = 5tet…

A: Explanation of the answer is as follows

Q: 1 1² +49 When solving O a) I = [sen (0) de Ob) I=tan(0)de O c) I = cos(0)de I= O d) I-sec(0)de I=…

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Q: For the next three exercises, use power series operations to determine the Maclaurin series for the…

A: Given

Q: (a) Find the slope of the line through (-7,5) and (9,-3). (b) Based on the slope, indicate whether…

A: Given :Points : -7, 5 and 9, -3

Q: 5. Find three 2 x 2 nonzero matrices A, B and C such that B C and AB = AC = 0.

A: To find the matrices A, B and C satisfying the given conditions.

Q: A utility pole has a guy-wire attached to it 3 feet from the top of the pole. The wire is attached…

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Q: Solve the given differential equation by undetermined coefficients. y" + 2y' + y = sin(x) + 4…

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Q: Show that there are no tangents to the curve f(x) = 6x3 + 2x2 that have a slope of -5.   Please…

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Q: c. Given f(x) = 2x - 3, g(x) = -4x² +9, h(x) = 4x² - 12x +9; find 1. f(x)* g(x) 2. h(x)/ f(x) 3.…

A: Dear learner, As per our guidelines, we can provide the solution for first three parts only. Kindly…

Q: A) Find area bounded by y = 0, y = √x - x² using double integration.

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Q: 11. Draw a high-quality graph by hand on graph paper for the function f(x) = 2x³ + 6x². Your work…

A: Given :  f ( x ) = 2x 3 + 6x2  find minimums , maximums and inflection points ,  And intercepts

Q: Use the properties of the definite integral to express the definite integral of ƒ (x) = 6x³ − 4x² +…

A: Given :f(x)=6x3-4x2+2x-3interval [ 1, 3 ]