Find the slope of the tangent line to polar curve r=5sinθ at the point (5/2,π/6).

Q: Find a power series for the function, centered at c. 1 h(x) 1 C = 0 8x' h(x) = n = 0 Determine the…

A: We have to find the power series and interval of convergence.

Q: 2. Determine whether the statement is True or False. If it is false, explain what makes it false, or…

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Q: 3. The derivative of /(x) = In x at x = 3 when hourrent = 0.001 and hprevious = 0.002

A: Given problem:- 3. The derivative of f(x) = In x at x = 3 when hcureent= 0.001 and hprevious = 0.002…

Q: 20 Evaluate the integral dx dy by reversing the order of integration. NOTE: Enter the exact answer.…

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Q: Find the dy/dx of the parametric equations given: x= 2t² – t and y= t³ – 2t – 1

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Q: Find the directional derivative of f at P in the direction of a. f (x, y) = 17 tan Р(-18, 18); а %3D…

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Q: Find all the values of x between 0 and ë where the tangent line to the graph of y = sin (x) cos (x)…

A: We will use the concept of differentiation to solve this.

Q: . The line segment from (1, –1,3) to (0, –3, 1) forms a diameter of the sphere S1. Find the…

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Q: Where is each function continuous? (b) f(z) = sin (1-r) I+3 (c) f(r)= In (d) f(r) = 12+5r +6

A: Topic:- function

Q: A businessman borrowed Php2,500,000 for 5 years at 5.5% simple interest. What amount must he pay at…

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Q: Use a parameterization R(u, v) of f (x,y) = xe*y to find the tangent plane to f(x, y) at the point…

A: Tangent plane at (x1, y1) to f(x, y) is given by below:

Q: Let f(x) = 10x6 + xx² + e2x. Compute f()(x). (Use symbolic notation and fractions where needed.)…

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Q: Find an equation of a line through the point (-1,3) making an angle of 45 degrees with the line…

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Q: Question Determine the interval(s) for which the function shown below is decreasing. 2 6-6 2 3…

A: We have to find  interval in which function is decreasing.

Q: Find lim f(x) for the given piecewise function. x-6 2x + 1 if x 6 If the limit does not exist,…

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Q: 2 x²+yi -I -VI-2²

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Q: Consider the following planes. 5x + 2y – z =22 X- 4y + 2z = 0 (a) Find the angle between the two…

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Q: 99. Find the point of inflection of the curve y=(9x^2-x^3+6)/6. a. 3,10 b. 2,8 с. 3,8 d. 2,10 100.…

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Q: Find the arc length L of the graph of r(t). 1 .3 r(t) = i+t j+¬V61² k, 2 <153 L =

A: Solve the following

Q: 40senz are solutions of the differential equation senr It's known that y1(x) 2(z) : 4z2y" + 4ry' +…

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Q: A factory selling cell phones has a marginal cost function C(x) = 0.01? -3x + 229, where z…

A: Given problem:- A factory selling cell phones has a marginal cost function C(x) = 0.01x2 - 3x + 229…

Q: Using the method of cylindrical shells, set up but do not evaluate an integral for the volume of the…

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Q: Finding Partial Sums In Exercises 5-10, find the sequence of partial sums S, S2, S, S and Sg. 5.…

A: 6. 12.3+23.4+34.5+45.6+56.7+.....10. ∑n=1∞(-1)n+1n!

Q: y = 6x³ – x-4

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Q: Find the extremum of f(x.y) subject to the given constraint, and state whether it is a maximum or a…

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Q: True/False Indicate whether the statement is true or false. 9. A normal vector to a line is parallel…

A: We have to state whether the given statements are true or false: Statements are as follows: 9. A…

Q: If the following function f(1)= are , for some non zero constant real numbers a and b a? equals 1662…

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Q: Find the extremum of f(x.y) subject to the given constraint, and state whether it is a maximum or a…

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Q: If we have that f: R → Ris a continuous function , in which f'(7) = 6 and f(7) = -2 an equation of…

A: We have to find out tangent line

Q: NOTE: Enter the exact answer as an improper fraction if necessary. A =

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Q: Use the Shell Method to compute the volume of the solids obtained by rotating the region enclosed by…

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Q: Find the divergence of F(x, y, z) =(a -1 Y, y? + 1' 3xz2 + 2y ) at (2,0, – x COS

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Q: Consider the expression: ey = 4x + y* , In which y is an implicit function of x , after derivation…

A: Given problem :- ey =4x+y4 , find y'

Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does…

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Q: Suppose the Sunglasses Hut Company has a profit function given by P(q) = – 0.02q + 5q 38 where q is…

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Q: Find the arc length of the parametric curve. x = e', y = et, z = V2t; 0<t< 4 L = 54.6

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Q: E-10: Let f(x) be a non-constant polynomial satisfying the relation f(x).f (y)= f(x)+f(y)+f(xy)-2,…

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Q: 4. Show that a b

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Q: Set up a triple integral for the volume of the solid. Do not evaluate the integral. The solid…

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Q: Compute f(x)dx (6 points) f(x) = { 2x if x<1 4 if x21

A: In this we have to do the integral of given function so I'm providing hand written solution for this

Q: The equation of the tangent plane to this ellipsoid at (1, –2, –2) is The vector parametric form of…

A: Let's find.

Q: Question * Using the Nth term test for divergence 1 2n + 14 n=1 diverges since lim is equal to 1.…

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Q: Consider the equation y" + ay' + by = f(x) the constants a and b are real and different from zero,…

A: The given problem is solved below in detail.

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: Given region is bounded by the function y=16x-2x2 and y=0 and rotating about y axis.

Q: please

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Q: 3. If f and are continuous functions with f(3) 4 and lim 2f(x)-9(r)3D5, what is g(3)?

A: To evaluate the value of the function

Q: Write an expression for the nth term of the geometric sequence. Ther a = 6, r = 1 n = 12 2 an %3D…

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Q: A one-product company finds that its profit, P, in millions of dollars, is given by the following…

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Q: Compute the derivative y dy dx y = 7x3 – x-4 (Express numbers in exact form. Use symbolic notation…

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Q: Use a double integral to find the volume of the indicated solid. 9 z = 9–2 y 2 y=2 4 X=4

A: Consider the solid