Evaluate the following limits 1. lim (2x+x) x → +00 e2x +In x

Q: Find the formula for the sequence below: -5,15,-45,180,...   a an=-3(-5)n-1 b an=5(3)n-1 c…

A: We have to find the formula

Q: Given: cos 3y + sin 2x 2 cos 2x 2 O -3 sin 3y-3 -2 cos 22-2 O -3 sin 3y 3 O -2 cos 2x-2 3 sin 3y 3 2…

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Q: Find the area of the region bounded by: 21. x + 1 = 0, x-3 = 0, y + 4 = 0 andy-5=0. 22. 2x + 3y = 6,…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 5. sech 2x tanh 2x dx sech

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Q: Find the equation of the family of curves having the given slope, and the equation of the curve of…

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Q: 3. Σ7ne-² (Integral Test) n=1

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Q: 5. Find the area bounded by y = sin √x and y = 0 on the interval [0, π²].

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Q: 1. f³₂ (x² − 3) dx -2

A: Given :∫-23x2-3dx

Q: A particle moves along a straight line from the origin (at t=0) with the given velocity v. Find the…

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Q: 3. Find f'(a) if f(x)= e7x 2x + sin³ x

A: In this question, we want to differentiate the given function f(x) with respect to x.

Q: A real estate firm estimates that the value of a certain property will be given by the function V…

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Q: Convert the degree measure to radian measure. Round to three decimal places. −46.23°

A: Convert the degree measure to radian measure. Round to three decimal places. −46.23°   Please show…

Q: 3. SET-UP the definite integral that will give the area of the region specified using (a) z as the…

A: topic- area bounded by curves

Q: Sketch the graph of y = x-2 (x+3)²

A: The horizontal asymptotes by comparing the degrees of the numerator and denominator. Vertical…

Q: (Requires a short but nontrivial geometric argument.). Let ABC be a triangle with angles…

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Q: II. Find the value(s) of x (or the interval of convergence) 2. Σn=0 for each of the following power…

A: The power series is  ∑n=0∞ (-1)n+1(x-5)nn·5n

Q: Com A real estate firm estimates that the value of a certain property will be given by the function…

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Q: dy dx = x+1 2(y+3)

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Q: A particle is moving along a horizontal line such that its velocity in m/s is given by v(t) = 2t²…

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Q: Charles plots the point with the polar coordinates (-5,-). How does he plot this point? Drag a value…

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Q: (b) Find the dimensions of a box with a square base with surface area 16 and the maximal volume.…

A: The second question has been solved as per the request of the student.   This question can be solved…

Q: Integrate the following (3x + 5)dx 1. S (x - 1)(x² - 1) -

A: Given:∫(3x+5)dx(x-1)(x2-1)Perform Partial…

Q: 65

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Q: 6. Find the area bounded by y= In x, y = 0 and x = e.

A: Area of a curve y=f(x) bounded by x=a, x=b is given by, A=∫abf(x)dx ln(e)=1, ln(1)=0

Q: Determine whether the infinite geometric series is convergent or divergent. If it is convergent,…

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Q: valuate £₁² (2x + 3e* − 1) dx a. 12.43 b. 13.45 c. 14.24 d. 15.23

A: We will solve the problem.

Q: 3. You are tasked with designing a cylindrical can. The material for the top and bottom of the can…

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Q: Draw a direction field for the differential equation y'= (y - 9)². Based on the direction field,…

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Q: Simplify the expression (1 - i)(√3+i) (1 + i)(√3-i) and express your answer in polar form where r> 0…

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Q: The height of a projectile launched into the air is given by f(t)= - 16t² + 220t + 10, where t is…

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Q: In this problem we will prove one orthogonality relation used in Fourier analysis. a) Show that…

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Q: Sketch the graph of r = 0 90° +2

A: To sketch the graph of r=θ90°+2.

Q: Perform the integration. 3 [² (13² - 11 + 13* - 31) dx

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Q: Find T,N and k for the curve:

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Q: (c) 0$ y = cos (√√x² +1) (d) y 2x 2x +1

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Q: 4. A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15…

A: Using derivative

Q: 1 вхось xа(1 — x)bdx - = 6xº1 Bx®1 - x)dx /0

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Q: Questions 1-4: The graph of a function y = f(x) on the interval [-3, ∞) is shown below. Use the…

A: Given.

Q: I. Determine the convergence of each of the following series using the indicated test. In number 4,…

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Q: What is the exact value of sin(67.5°)cos(22.5°)?

A: Solution-

Q: It is projected that the population of a certain town will be P(t) = 2t+4+³/2 + 5000 where P(t) is…

A: Rate of increase of population=P(9)-P(0)9-0

Q: If f(x)=5x(sinx+cosx), find f′(x) =

A: Product Rule of differentiation : du.vdx=u.dvdx +dudx.v dxndx=n.xn-1 dsin(x)dx=cos(x)  and…

Q: For the function f(x,y) = √y² + 5x², find f(2, - 5), f(− 1,2), f( – 3, – 5), and f(0,9). f(2,-5)=…

A: Given query is to find the value of the function at indicated points

Q: Find the linear approximation of the function g(x) = 1 + x at a = 0. g(x) * Use it to approximate…

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Q: Evaluate the integral of 3dx/(2x^2 + 4) from 0 to 0.2 *

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Q: For which value of a is the differential equation (y² + axy³ )dx + (Ky²x² + 2xy) dy = 0 exact

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Q: 6. csch x dx

A: To find the integral of the given function.

Q: Convert the rectangular equation x2 = −2y2 + 5x2 y2 to polar equation

A: The rectangular equation is x2=-2y2+5x2y2

Q: Let f(x, y) = (x³ − x)(y² – 1). Find fry(x, y).

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Q: Given Cost and Price (demand) functions C(q) = 120q+40000 and p(q) = -2.4q+800, what profit can be…

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