Q.3// Solve the following second order differential equation: *+ 25x = 0

Q: 225 Find the equation for the tangent line to f(x) = I at the point (5, 45).

A: given function f(x)=225x

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A: The equation of curve y=-x2+5x-1

Q: 5. Evaluate the integral using integration by parts. (5x² - 4x) e²x dx (5x² - 4x) ²x dx = [

A:

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A: Thickness of paint = 0.08cm Diameter of hemispherical dome is 70 meter

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A: The function is given by fx = x3-12x+4 To determine: The interval of increase and decrease.

Q: The expression ( x²y-¹2-2 (xy)-42-3 -4 = x²y³zt where:

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Q: Find the inflection point, if it exists, of the function. (If an answer does not exist, enter DNE.)…

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Q: Use the method of Laplace transforms to solve the given initial value problem. Here, x' and y'…

A: The Laplace transform is a mathematical tool used to transform a function of time, typically a…

Q: ds dt |₁=5 m/s

A: We know that the speed formula =sqrt((dx/dt)^2+(dy/dt)^2)

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Q: 55. Show that 5₁²x -3 x-³ dx. 1 dx x³ +4 converges by comparing with

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Q: (3) Find the derivative using = lim dx h→0 f(x+h)-f(x) h for f(x) = x³ - 1

A: As per the guidelines I am supposed to solve only one question at a time. Please repost the other…

Q: Classify each singular point (real or complex) of the given equation as regular or irregular. 2x²y"…

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Q: A Box Constracted Card or Cutting Corners with an from a board out T each and find the largest open…

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Q: 1. Consider the function f(x, y) = x²y - 2xy − 3y². Find all critical points of f, and classify…

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Q: 0.021 The number of visitors P to a website in a given week over a 1-year period is given by…

A: P(t)=120+(t-85)e0.02t

Q: Find an equation of the tangent plane to the given surface at the specified point. z = y ln(x), (1,…

A:

Q: How did you choose pi/2, -pi/2 when setting it equal to 3 theta.

A: How did you choose : 3θ = π/2 and –π/2

Q: Match the polar equation with the graphs labeled I-VI. 7 1 - sin(0) O O O I III V r= O II IV VI y…

A: We can convert polar equation to cartesian form by using the following substitution. x=rcos0y=rsinθ…

Q: 6 2 (0, 3) The graph of f(x) B) lim f(x) = = x→3+ C) f(3) = = 2 (3, 2) (3, 3.141) 2x² +3 sin(x) + 3…

A: fx=2x2+3x≤0sinx+30<x<3-2x+8x≥3 And Graph of function

Q: 8) Find the area under the sin curve from 0 to it.

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Q: Test the series for convergence or divergence using the Alternating Series Test. √n 4n+ 5 Identify b…

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Q: Compute the derivative of the function y = 6 sin¹(x) at the point x = 1. (Use symbolic notation and…

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Q: Write an integral that represents the area of the shaded region of the figure. Do not evaluate the…

A: Graph

Q: A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a…

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Q: The four sequential sides of a quadrilateral have lengths a = 5.2, b = 8.4, c = 10.8, and d = 12.4…

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Q: Graph the polar curve r = Jo д - 4 - 2 sin 0 Select a curve and use the point(s) to adjust:

A: r=-4-2sinθ

Q: (4) f(x+a)-f(x) Find the derivative of f(x) = x² + 3x - 7using = lim dx a-0 (x+a)-x

A: 4.

Q: Calculate the iterated integral. 64 8 [** [* (* + X) Jv dx dy

A: Double integral.

Q: Find the vertical, horizontal, and oblique asymptotes, if any, for the given rational function. x-1…

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Q: o Find the polar equation of a line parallel to the line r cos (0 - (Use symbolic notation and…

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Q: Find the sum of the infinite geometric series. Σ19 (3)*-1 27 2 Ο -27 Ο -26 Ο -31 ●

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Q: 10. Solve the inequality (3-x)(2x+1) 2-1 >0 algebraically and graph the solution set.

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Q: x²-16 3 A) -4 and 4 and- 2 C) -4 and 4 B) 4 D) Nonede D) a 10)

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Q: Suppose you use a tracking telescope to follow a rocket. Suppose you are also 2000 meters from the…

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Q: Let g(x) = x² + 7x + 3. Evaluate and simplify completely the following difference quotient.…

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Q: Consider the following curve. r² = sin(20)

A: We have to find out the area of the shaded region.

Q: Use the Root Test to determine whether the series convergent or divergent. Σ(13) Identify an…

A: Given: ∑n=1∞n2+37n2+9n  We are required to find: If the series is convergent or divergent(using the…

Q: lan Dan and Tom share a sum of money. Ian received 5/6 as much as Dan. The ratio of lan's share to…

A:

Q: Consider the given vector field. F(x, y, z) = xyz i-x²y k (a) Find the curl of the vector field.…

A: Given vector field F( x , y , z ) = xyzi - x2yk

Q: A business analyst starts at $45,000. She receives a 5% raise at the end of each year. What is her…

A: P=$45000Rate = R= 5% =0.05Time=t=6 years

Q: 3. Find the rate of change in the demand x of a product if the price is $2 and the demand function…

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Q: Evaluate sin x -dx 1³ x indefinite integral as an infinite series.

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Q: 3) |x| = 7, y = 8, and|x - y = 10, determine | x + y. Hint: sketch out these 4 vectors on the same…

A: We know that the vector parallelogram rules  ||A+B||^2+||A-B||^2=2||A||^2+2||B||^2

Q: Find the volume of the solid formed when the region bounded by the graph of f, the x-axis, and the…

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Q: Find the area of the surface. The part of the plane 3x + 4y + z = 12 that lies inside the cylinder…

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Q: Compute for dy dx

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Q: Use the Laplace transform table and the linearity of the Laplace transform to determine the…

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Q: 1. Find the volume of the solid generated by revolving the region bounded by y=3x², y=0, and x=3…

A: The volume formula int_a^b pi*r^2 dx

Q: Find the derivative of the function f by using the rules of differentiation. f(x) = 3x³ - 9x² + 8.…

A: The given function is  f(x) =3x^3-9x^2+8 As we know that d/dx(x^n) =nx^(n-1)  And differentiation of…