A ball is shot from the ground straight up into the air with initial velocity of 43 ft/sec. Assuming that the air resistance can be ignored, how high does it go? Hint: The acceleration due to gravity is 32 ft per second squared.

Q: Calculate whether the differential equation is exact or not and Find the general solution.

A: The given differential equation is:x2+2x+ydx+2dy=0We need to check whether the equation is exact or…

Q: Prove the following by Mathematical Induction 1. 1/1(2) + 1/2(3) + 1/3(4) +...

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 5 + 3y, 1 <…

A: We have to find the surface area of the solid.

Q: Find the parameter k such that the function y cos(kx) satisfies the equation y + 5y" = 0.

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Q: Does the series diverge? Converge or tin ta)^

A: We need to determine if series converge or diverge.

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Q: 17. у dx — (х + бу?) dy 3D0 (х + бу?) dy %3D 0-

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Q: A firm estimates that it will sell N units of a product after spending x dollars on advertising,…

A: Given problems:- a) A firm estimates that it will sell N units of a product after spending x on…

Q: Determine whether the sequence is increasing, decreasing, or not monotonic. (Assume that n begins…

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Q: Consider the real sequence {an} given by an = In(n + 1) – In(n +2), n e Z20 = NU {0}. Justify…

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Q: de 1+sin e+ cose CO

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Q: The multiple choice answers to choose from are A) (lnx)^2 B)2x^(lnx-1) lnx C) x^lnx-1 lnx D) 2lnx/x

A: We can simplify the answer: 2xlnxlnxx=2·xlnxx·lnx=2·xlnx-1·lnx  Because xaxb=xa-b=2xlnx-1lnx

Q: 4. Find the integral of your answer in problems 2a and 2b. CO

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Q: This exercise uses the population growth model. A certain culture of the bacterium Streptococcus A…

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Q: 14. Given the vector form of a line in three-space to be [x, y, z] = [2,6, – 3] + t[4,10,6], find a.…

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Q: Find all first-order partial derivatives of the given function. + ye2= (b) g(s, t) = s tant + log2(s…

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Q: x² – 2x – 1 dx (x – 1)2(x² + 1)

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Q: Calculate the iterated integral. 6. x/2 (y + y2 cos(x)) dx dy Need Help? Read It Watch It

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Q: Solve for fxx, fxy, fyx and fyy given f(x, y) = 2 ln(x − y).

A: The given function is:fx,y=2 lnx-y.We need find fxx, fxy, fyx and fyy

Q: E) Find the line's equation which passes through the points (2 , 5), (-3, 1)?

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Q: 6 of 19 Write the equation of a circle with centre (-8,-3) which is tangent to the x-axis. O (x –…

A: A detailed solution is given below

Q: Two cars are initially 1200 miles apart. At the same time Car A starts driving at 35 mph to the east…

A: Given ,  Two cars are initially 1200 miles apart  At the same time Car A starts driving at 35 mph to…

Q: リ=ー"-4), find a) The x-intercept and the y-intercept b) The interval where the function is…

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Q: 1. Lets say Q(x) = 5x + 2 P(x) = 3x2 - 5x +1 Find (a) Q (-3) (b) P(5) (c) 5P(x) – 20(x) (d)…

A: Let's find.

Q: Determine the indefinite integral | 5x4(x5-6)8 dx by substitution. (It is recommended that you check…

A: Let's find.

Q: y²dx + (xy – 1)dy = 0

A: First of we will check whether given DE is exact or not

Q: 7. Find ſxsec¯'xdx using integration by parts made simple or otherwise.

A: Given ∫x sec-1x dx To find integration

Q: Find the area of the region. See Examples 1, 2, 3, and 4. f(x) = (x – 5)3 g(x) = x - 5 y 1.5| 1.0…

A: This question can be solved using the concept of area under curves.

Q: The point (4, k) lies on the ellipse 32 y? = 1. 18 Which of the following could be a value for k? 0…

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Q: Consider the graph and determine the open intervals on which the function is increasing and on which…

A: Here to of the function is at point (1,5), On left side function is increasing ,and at right side…

Q: Evaluate the integral sin x dx (2 + 3 cos x)2

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Q: Evaluate the integral (2x + 6)dx x² – 2x + 17

A: Given ∫(2x+6)x2-2x+17dxTo evaluate integral:

Q: Evaluate the integral (Trigonometric Substitution) x*dx (x² + 9)2

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Q: Find the indefinite integral and check the result by differentiation. (e5+ sec e) de

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Q: (b) А — В (с) 2A (d) 2A – 5B

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Q: 4. 2 cos(2x – y) dx – cos(2x – y)dy = 0 - %3D

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Q: х2 — Зх — 7 dx (x2 + х + 2)(2х— 1)

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Q: Let f(x)=5x/2 - ex . Find the value of x for which f''(x) equals zero.  A. 0 B. 5e C. ln5 D. e5…

A: Solve for x by differentiate f(x) with respect to x.

Q: Suppose z is a function of x and y satisfying the equation rey + ye" + ze = 1. Use implicit dz dz…

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Q: An equation of the tangent line to a curve at the point (3, 5) is y = x + 2. if at any point (x, y)…

A: To find the equation of curve

Q: Find the general indefinite integral. (Use C for the constant of integration.) | (x2 + 2x - 3) dx…

A: The objective of the question is evaluate the indefinite and definite integral.

Q: Find the nine roots of -256 – j256/3.

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Q: The functiof(x) and it’s first and second derivative are given: A) Domain of f(x) B)y intercept is…

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Q: Use the Root Test to determine whether the series convergent or divergent. 00 n2 + 6 Σ 2. 5n + 2 n =…

A: Given: Here, an=n2+65n2+2n.

Q: Determine whether the diff eq. is exact. If it is, find the general solution.

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Q: Rates of Change: Oscillating Spring At Answer the following question, and give a written…

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Q: 2. Write the given (total) area as an integral. (vde a. The area above the x- axis and below y = 4–…

A: Here we have to find the area.

Q: Suppose there are 10 points in a plane such that no three points are collinear. How many distinct…

A: Given; There 10 points in a plane such that no three points are collinear

Q: 6. 2y²e»² dx + 2xye»*dy = 0

A: