Find r'(t), r(t0), and r'(t0) for the given value of t0. r(t) = (1 + t)i + t3j, t0 = 1 r'(t0) =

Q: Locate the absolute extrema of the function on the closed interval. In x, [1,4] 7x g(x) = minimum…

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Q: Find the area of the surface generated when the given curve is revolved about the given axis. 1 3 y…

A: y=8x13, for 0≤x≤18, about y-axis

Q: Minimize c = x+y+z+ w subject to 5x - y + w ≥ 4,000 z + w≤ 3,000 x + y s 700 x ≥ 0, y ≥ 0, z ≥ 0, w…

A: Min c=x+y+z+w5x-y+w≥4000       z+w≤3000x+y    ≤700x≥0,y≥0,z≥0,w≥0

Q: 3x e 1-ezx dx

A: Given, ∫ e3x1-e2xdx

Q: No calculators. Find the exact length of the curve. 0≤x≤l y=2+2x³/2,

A: Length of the curve  =∫ab 1+f'(x)2 dx .

Q: A tenant dropped a spoon from the top floor of her apartment building and it fell according to the…

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Q: Compute the given improper integral. Enter the exact value of the answer. 1 /x² 400 29 So - dx =

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Q: No calculators. Find the exact length of the curve. y=2+2x³/2, 0≤x≤1

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Q: Find the sum of the series: n=0 2-1 (-1)"64"- n!

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Q: True or False: We have Select one: True False -8 √xdx = 64 3

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Q: 6. Consider the function f(x, y) = cot ¹(1+x) — 2e¹+³y If x = s²-t² and y = 3t+tan(1-s), use the…

A: Let's evaluate given partial derivative.

Q: 3. The radius of a sphere ball is measured at r= 25 cm. Estimate error in the volume and surface…

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Q: Find r'(t), r(t), and r'(to) for the given value of to. Then sketch the space curve represented by…

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Q: Find all solutions of the equation in the interval [0, 2π]. 2cos2xcosx-2sin2xsinx = 1 Write the…

A: Here, the given equation is: 2cos(2x) cos(x)-2sin(2x) sin(x)=1⇒cos(2x) cos(x)-sin(2x)…

Q: Problem 4. A particle moves back and forth along a straight line with a velocity of v(t) = 1-²…

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Q: Let f(x)=(3x(^2) -4x+5)(^100) -((2x+1)/(x-3))^5. Calculate df/dx

A: We can find the derivative as below.

Q: Use Green's Theorem to Calculate the Line Integral ſy²dx + x²dy, where c is the triangle o vertices…

A: Given that, the line integral is ∫y2dx+x2dy and the vertices of the triangle is 0,0,4,0 and 4,4. By…

Q: 16. A small tie shop finds that at a sales level of x ties per day its marginal profit is MP(x)…

A: We need to find P(x).

Q: II. Solve the given differential equations. (x+y-4) dx - (3x - y - 4)dy = 0; when x = 4, y = 1 (6xy…

A: We have to solve given DE.

Q: Find | 22 x²z ds, where C is the line segment from (0,4,-6) to (2,9,-5)

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Q: 21) In a triangle ABC, B = 65°, C = 45° and a = 10. The measure of angle A is : a) O 90° b) O 80° c)…

A: I am attaching image so that you understand each and every step.

Q: 19. For a given function, f(r)=³-152² +48x+2. (a) Find the interval(s) on which is increasing. (b)…

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Q: Problem 1 Find a linear differential equation with constant coefficients satisfied by e²x, e*, e³x,…

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Q: fror Find the area of the surface that results when y= around the x-axis from x = 1 to x = 2 2x² 3…

A: We have to find the surface area of the solid.

Q: Find the curl of the vector field F curl F = (2y cos(x), 5x sin(y))

A: F = (2ycosx , 5xsiny) find curl F =?   curl F  = dF2/dx - dF1/dy here  F1 = 2ycosx  F2 = 5xsiny now…

Q: 800 100-ex/2 50 es 9.621.

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Q: 15. Show that the equation, ³ + e* = 0 has exactly one real root.

A: we have x3+ex =0to check number of roots we can draw graph of both and check number of intersection

Q: Consider the given function, h(x) = 3x² - 15x+4. (a) State whether the graph of the parabola opens…

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Q: Determine the location and value of the absolute extreme values of f on the given​ interval, if they…

A: To determine the location and value of the absolute extreme values of f on the given interval, if…

Q: 4 Determine -2 u tv and Give a is i and v и So Keat orthogonal to ²-5²³ lutô| = |a²|+12²1…

A: Given the vectors u+v and u-v are orthogonal and  u+v=u+v To find u and v .

Q: f(x) = 5x 2x - 1 Español 1 Find f¹(x), where f¹ is the inverse off. Also state the domain and range…

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Q: Question 2 Consider the point P(-2, 1, 4) and the vectors a = and 6=. (a) Find the unit vector u…

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Q: 414) Find the remaining sides of the right triangle if sin B = 8 12 16 20 a) b= b) b = c) O ○ d)…

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Q: Find all solutions to 2 sin(0) 0= = - - 1 on the interval 0 ≤ 0 < 2π Give your answers as exact…

A: We can find the answer as below.

Q: Question: The two equal sides of an isosceles triangle measure 95 centimeters and the angles that…

A: The two equal sides of the isosceles triangle are, a=b=95 centimeters The angle that subtend them…

Q: 2. y(x-y²)dx + x(x++y²)dy = 0

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Q: Prove that for any integer n if 3n+ 2 is even, then n is also even.

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: Use differentials and the graph off to approximate the following. (Round your answers to two decimal…

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Q: Determine the location and value of the absolute extreme values of f on the given interval, if they…

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Q: Graph of the function. Show all 7 steps. h(x)=(x+1)2-2

A: I am attaching image so that you understand each and every step.

Q: Find the radius of convergence and the interval of convergence. xk k(k + 5) Radius of convergence:…

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Q: (a)i Find a vector equation and parametric equations for the line that passes through the point A(5,…

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Q: c) [. The intersection of the sphere B and the xz-plane is (x - 2)² + (z + 1)² 2)² + (z + 1)² = 9.…

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Q: (d) A√x X²-2 3z +9 use quotient Rule use quotient Rule

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Q: Let f(x) = be a piecewise function. Evaluate So fo f(x)dx= 3x²+2, 2x - 3, if x < 2 if x ≥ 2

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Q: Determine the location and value of the absolute extreme values of f on the given​ interval, if they…

A: The function is given as , fx=8x33+14x2-16x find the location and value of the absolute extreme…

Q: The given family of functions is the general solution of the differential equation on the indicated…

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Q: Find y dV, where E is the solid bounded by the parabolic cylinder z = = 2 and the planes y = 0 E and…

A: The solution is given below

Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

A: Topic = Series

Q: (a) Find a vector equation and parametric equations for the line that passes through the point A(5,…

A: We have to find solution for given questions.