Q1. Calculate the area of the region lies inside the diagram (r= 4 cos 20) and outside the circle (r = 2).

Q: Evaluate the given limit. Show your complete solution. limo(-x ln(sin(4x² + x)))

A: The given limit is limx→0-xlnsin4x2+x. We have to solve the limit using L'Hpotial's rule.

Q: The number of bacteria in a refrigerated food product is given by N(T) = 23T² – 96T + 12, 5 < T < 35…

A: The number of bacteria in a refrigerated food product is given by N(T) = 23T2-96T+12,  5&lt;T&lt;35…

Q: Q1: Find the Fourier coefficients and Fourier series of the triangle function f(x) defined by

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Q: 1. Determine whether the series n=1 3n+1 ln(n+1) is convergent or divergent.

A: : since,1&lt; ln(n+1),for n&gt;2 so, 0&lt;(n^2)/(((3^(n+1))*ln(n+1))&lt;n^2/n^4=1/n^2,  since…

Q: Evaluate: lim, 1+ (-1)2 tan(x)

A: Evaluate the following limit

Q: Question 2 (a) Find the derivative of the function. x3 F(x) = sin(u²) du (b) Find the area of the…

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Q: On the graph of the function f(x), shown below in blue, choose whether there are zero, one, or two…

A: Horizontal asymptote

Q: A stone, projected vertically upward with initial velocity 112ft/sec, moves according to s = 112t −…

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Q: Find the limo (cos x) = Show your complete solutions. No shortcuts.

A: Given,  limx→0cos x1x2

Q: Given the differential equation y'' − 3y' – 4y = - 2 sin(2t), y(0) = 0, y'(0) = - = - 1 Apply the…

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Q: Evaluate: lime 1-sin 0+cos 0 sin 20-cos 0

A: The objective is to evaluate the limit.

Q: What is the lim (3)¯ I 7 sec (7x) cos(3x)?

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Q: Given a vector function (a) Find the domain of r(t). (b) Find the limit lim r(t). t→1 (c) Find the…

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Q: 5. 1-cos2y 1+cos2y dy

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Q: 30 Which one of the following is the gradient of the tangent line at the point (5, 1) on the graph…

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Q: Consider the following graph of a function f(x) 7 A. For what value(s) x is f discontinuous? If f is…

A: As per our guidelines, I can answer maximum three sub parts of a question. Since there are multiple…

Q: Give a general solution of the differential equation y"–9 y = −2t cos 3t

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Q: Evaluate: limt. +00 ln 5t 4t²

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Q: Boyle's Law for the expansion of gas is PV C where P is the pressure (in weight units per square…

A: Follow the procedure given below. Here you have to differentiate with respect to pressure.

Q: What is the limo+ (√In(x))? For answers that are fractions infinity ti infinitu write... in decimal…

A: We are asked to find the limit of the function.

Q: Find y' y = e2x - e3x e4x

A: This question is based on diffrentiation of exponential Function.

Q: y = In x (x-5)ez-1

A:

Q: Let f denote a piece-wise defined function whose graph on the closed interval [-3, 3] is sho below:…

A: Here, the function is continuous on: (-3,-1)∪(-1,3)

Q: lim cos x x-0 , which among the following should result, in equivalent form, before L'Hopital's Rule…

A: To evaluate: limx→0 cosxx Let y= limx→0 cosxx ⇒y= limx→0 cosx1x

Q: Solve the following initial value problem using Laplace transforms. d² y dt² -9y=4e³¹; y (0) = 0,…

A: d2y/dt2 - 9y =4e3t; y(0)=0, y'(0)=-1.

Q: (i) Find the linear approximation of the function f(x, y) = 1 - xy cos πy at (1, 1) and use it to…

A: Here, the given function is: f(x,y)=1-xycos πy To find the linear approximation of the function. For…

Q: For the equation y I. Domain 2. Symmetry 3. Intercepts (if any) YA In (x-6)ex, find; =

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Q: For the following exercises, draw the region bounded by the curves. Then, find the volume when the…

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Q: 5 Sketch an angle 0 in standard position such that 0 has the least possible positive measure, and…

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Q: The area in the first quadrant under the curve y = e-x is revolved about the x-axis.  Find the…

A: Topic = Volume

Q: The 7th derivative of ƒ(x) = 3ñx³ – 12x4 + 7x³ − 11x² + √5 with respect to a is

A:

Q: Given the piecewise function f(x) = Why is f not differentiable at x = 5? Of is continuous at x = :5…

A: This question is based on continuity of function.

Q: Identify and sketch the graph of y=x² + 1 in R³.

A: This question can be solved using the concept of parabola.

Q: What is the lim [(ln(2x - 4)) - (ln(x + 3))] 818 ? If your answer is a Whole Number Fraction (+)…

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Q: What is the lim 0 (sing - )? If your answer is a Whole Number Fraction (+) Positive Infinity (-)…

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Q: Find an equation of the tangent plane to the given surface at the specified point z = √√√xy, (3, 3,…

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Q: 12. DETAILS ZILLDIFFEQMODAP11 1.R.001. Fill in the blank. The symbol C₁ represents a constant. d =…

A: The solution is given below.

Q: Match the given differential equation with one or more of the solutions. (Select all that apply.)…

A: Substituting the given values of y in the differential equation

Q: 12. The graph of y=x² between x=1 and x=3 is rotated completely around the x-axis volume generated.

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Find the solution to the differential equation below such that y(0) = 14 y' = 10xy - 2x y(x) =

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 28 Which one of the following is the co-ordinates of the y-intercept of the tangent line to the…

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Q: ل 2 ل وه هه ** ** " سم Z || . 1

A: Given problem:-

Q: What is the limx→5 5x + 2? 3 5 1 27 1 3

A: To evaluate: limx→5 5x+23 Let y = limx→5 5x+23 y = limx→5 5x+213

Q: y=xe

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Which of the following is TRUE for all? All functions are continuous at all points in its domain.…

A: Given :   Continous and differentiable functions

Q: The area bounded by the parabola y2 = 4ax, its axis, and its latus rectum revolves  about the x-

A: Given: y2= 4ax

Q: What is S (x² + 2x)² dx? + x³ + ³x² + C 4 S (x² + 2x)²dx = ¹x¹ + x³ + 4 f (x² + 2x)²dx = (x² + 2x)¹…

A: We know, ∫xndx= xn+1/(n+1)

Q: m³ The volume of a large spherical balloon is increasing at a rate of 64 balloon's surface area…

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Q: Classify each differential equation as separable, exact, linear, homogeneous, or Bernoulli. Some…

A: See Explanation

Q: Aball is launched straight up in the air from a height of 7 feet. Its velocity (feet/second) t…

A: