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Q: Find the interval of convergence of the series. (3x)" * Σ n2. 10" n=1

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Q: For t > 0, a particle moves in the xy-plane with position vector (x (t), y (t)), where x (t) = te-t…

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Q: 1. 4x°dx (2-x*) ° 6

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

A: Given: y=x+6, y=x, y=0   From the given curve and lines the bounded region is as shown below; Now…

Q: y²dy Vy2+4 3.

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Q: (Easy) For the following differential equations, state the independent and dependent variables, and…

A: Here we have to find the dependent and independent variable order and the degree of given…

Q: Evaluate limx->3  x2 + 3x - 4

A: Solution :limx→3  x2+3x-4Split the limit using the Sum of Limits Rule on the limit as  x  approaches…

Q: V2+x² lim x-

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Q: Evaluate the definite integral two ways: First by a u-substitution in the definite integral and then…

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Q: Find the maximum and minimum of w(x, z) = 2xz + z^2 +1 in a region R bounded by x = 0, z = 0, and x…

A: The bounded region R is:

Q: t2+1 = 0 dv Vt- dt V+1

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Q: How 3 Find the absalute maxine and minima for the funCtion (4x-x) Cosy an the rectangular plate…

A: We have to find the absolute maximum and minimum.

Q: Find the points on the curve r = 1– sin 0 - where the tangent line is horizontal or vertical.

A: To find out the points on the given curve, where the tangent line is horizontal or vertical.

Q: The width of a rectangle is increasing at a rate of 5 cm/sec, while the length increases at 6…

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Q: 5. x= y= t2-1

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Q: A (4, 270°) (ounter= 909 120° 60° 150° 3.0° 180 0° 210° 330° 240° 300° 270°

A: We have to find the other  three coordinates.

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: The graph shows the rate of change of the revenue of a company from 2000 through 2015. dR dt 50 -…

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Q: -2 -1 1 3 6

A: Given Graph:- To find:-

Q: Use implicit differentiation to find dz/dx and dz/dy. yz = 2 In(x + z) dz ax ze dy II II

A: Consider a function f(x,y,z) .Then to find ∂f∂x ,differentiate f with respect to x taking y and z as…

Q: (a) A function f (x) is given as 1 x0 2x Evaluate lim f(x) numerically by constructing a table. (b)…

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Q: Assume f and g are differentiable functions with h(x) = f(g(x)). Suppose the equation of the line…

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Q: Evaluate the following limits analytically, if it exists. (a) Vx+14 – 1 lim x→-10 2x (b) 5x +7x lim…

A: Given problem:-

Q: ength of the curve 1 1 < x < 2. 6 10x3 +

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Q: Consider the function f(x) whose second derivative is f''(x) = 10x + 3 sin(x). %3D If f(0) = 2 and…

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Q: w³sec?xdx – (1 – 2w²tanx)dw = 0

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Q: Find the area of the surface obtained by rotating the curve x = 3 (y + 2)3/2, 1 <y< 2, about the…

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Q: In each part, use a scalar triple product to determine whether the vectors lie in the same plane.…

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Q: Question For the function f(x) given below, evaluate lim f(x) and lim f(x). X00 X--00 -4e f(x) = +9…

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Q: A particle travels along the x-axis such that its velocity is given by v(t) = = t.9 sin (3t). What…

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Q: Find y'. Given: y = -sin(4x)cot(4x) %3D

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Q: Given the function f(x,y)=3x² - y over the rectangular region, R = {(x, y): 0 < x s2,0 < y s 3}.…

A: we know, ∬Rfx,ydA=∫03∫02fx,ydxdy

Q: Project 8. Estimating Time of Death.  The purpose of this project is to practice reading a…

A: Note :- This is multiple sub parts question and according to our company guideline we can do maximum…

Q: 3- 4- f Cx,y) = 2 Lux +Lny-4X-y

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Q: 1+cos5x 4. Evaluate y'for y = and simplify the answer sin5x

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Q: III. SOLVE THE FOLLOWING INDETERMINATE FORMS e* +e* – x? – 2 1) Lim sin? x - x? 12+ x? 2) Lim X 00 X

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Q: Find the length of the arc of the given parabola: x²=4y from x=-2 to x=2

A: We know that the length of the arc of the parabola y=f(x) from x=a to x=b is given by L = ∫ab1+dydx2…

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

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Q: The derivative of sec(e) is tanx O 1) tan(e*") sec{e*™) O 2) tan(e**) sec(e*)x e** 3) tan(e)…

A: topic - derivative of a function

Q: For the functionf(x) given below, evaluate lim f(x) and lim f(). X-00 X→ー0 f(x) = –18x (x – 1) (x +…

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Q: 16 2. A light at the top of a 16 ft. pole. A man 6 ft. tall walks away from the pole at a rate of 5…

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Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method,…

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Q: Use the parametric equations of an ellipse, x = a cos(e), y = b sin(e), 0 se s 27, to find the area…

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Q: Activity 2. Let's Optimize! Directions: Solve the problems below. Show your complete solutions. 1.…

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Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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Q: For a given function f, what does f' represent? Choose the correct answer below. A. f' is the…

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Q: 10 Find the projection of u =-14 onto the -15 -4 -4 subspace W of R' spanned by -6 | and 6. 910 53…

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Q: Find the 24th derivative of y = -sinx

A: Topic = Derivative    The 24th derivative isy24 =-sinx

Q: Find the volume of the solid generated by revolving the region bounded by x2/3 + 1,0 < < 8, about…

A: Follow next step

Q: Integration by trgonometric substitution 1. S_dx (4x-x2) ³12

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