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Differentiation#19

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Math

Calculus

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Q: What is the solution to the initial value problem below? y′=5ex +8x3 +x2 +4x y(0)=3 Do not include "...

A: The given differential equation is, y′=5ex +8x3 +x2 +4x.

Q: 3. Given the function g(x) 8x defined on [-1, 1], determine if the function satisfies the Mean Value...

A: Given,

Q: e2h-1 if f'(a) lim-0 what is f(r) and what is a? h

A: Click to see the answer

Q: 1) The substitution u = tanx gives∫(sec2x.tanx)dx = ∫(x)du = 1/2.u2 + C = 1/2.tan2x + CThe substitut...

A: Yes, both integrations are correct by their respective substitutions.Reason:An integral of a functio...

Q: find the exact length of the curve of the equation below, show all work y = ln(sec(x)), with a range...

A: First, we find the dy/dx

Q: Find the point on the plane 4x+5y+x=11 that is nearest to (2,0,1). What are the values for x, y, and...

A: The equation of the plane is

Q: Use the derivative f'(x) = (x - 3)(x + 4)(x + 4) to determine the maxima and minima of f and the int...

A: f will be increasing if f'(x)>0. From the graph of f'(x) we see f'(x)>0 when x>3 [because a...

Q: Please help

A: Here we will make the use of series for sin(x2) to solve the given integral.The provided integral is...

Q: Differentiate the function. f(x) = (3x5 − 2)18

A: Consider the function:

Q: p(q)=2q2-4q+5; q=2 (a) Find the derivative, by using the definition. (b) Find the instantaneous rate...

A: Part (a)The derivative of p(q) at any point q, by using the definition, will be given by the express...

Q: An important question about many functions concerns the existence and location of fixed points. A f...

A: Given functions are f(x) = 17x cos x and f(x)=x. We graph them first and find where do they meet on...

Q: Use the Divergence Theorem to compute the net outward flux of the vector field F=<x2 , -y2, z2>...

A: The vector field is given as

Q: Sketch the region of integration and evaluate the following integrals. Please refer to attached imag...

A: Click to see the answer

Q: How do I solve this differential equation using P(x), Q(x) and v(x)?

A: The given differential equation is,

Q: Determine if y=e2x −x+1 is a solution to y′−2x=−3+2y.

A: The given differential equation is y′−2x=−3+2y.The solution of the deferential equation is given as...

Q: A theorem states that one local extremum implies an absolute extremum. Verify that the following fu...

A: The given function is,

Q: 7n 5-4n For the following answer blanks, decide whether the given sequence or series is convergent o...

A: (a)we are given a series as

Q: dy If y 22 x, then dx 9.7 1. O 22 0. O 5. N O O O OO

A: The given equation is y=22+x.

Q: When converted to an iterated integral, the following double integral is easier to evaluate in one o...

A: Given information:The given integral function is shown below:

Q: 3 dx = 1 2x 8 In 국 5 -4 In 2 In을 -2 In -8 In LOn LOn

A: Obtain the value of the integral as follows.The given integral is,

Q: please explain how to solve this problem

A: Consider x be the number of times the price is reduced by $0.05.

Q: How do you set up the line integral for y=x(6-x) boundary?

A: The vector field is given by,

Q: a. find the critical points of f on the given interval b. Determine the absolute extreme values of f...

A: Given information:The given function is .

Q: Is y=e6x −3x−2 a solution to the differential equation shown below? y′−6y=7x+3

A: Here given differential equation is:Find the solution of given differential equation and match the g...

Q: Consider the function g(x) = |(x^2 - 4)/(x+3)| do the following: a) Give the domain of the function ...

A: a) First obtain the singularity for the given function as follows.The denominator of the given fract...

Q: For the following function f, find the antiderivative F that satisfies the given condition. F(v) =

A: First, we find the general solution using integration.

Q: find the exact length of the curve of the equation in the picture below make sure to show all work

A: The given curve equation is,

Q: How can I get the result? Which is the result?

A: (a)Complete the table below analytically:

Q: I have trouble with second derivatives. I need help from my last step on please.

A: Given equations are,

Q: A mass hanging from a spring is set in motion and its ensuing velocity is given by v(t) = -2 sin (pi...

A: To find the position function we integrate velocity function and use s(0)=2.Answer(A): Position func...

Q: Find the arc length of the curve below on the given interval 3 /2 on (0,10] y 2x Which of the follow...

A: Click to see the answer

Q: An object is thrown straight up with a velocity, in ft/s, given by v(t)32t +53, where t is in second...

A: a)The given velocity function is v(t) = −32t + 53.In order to find the initial velocity, substitute ...

Q: How can I get the result? Which is the result?

A: Click to see the answer

Q: How can I get the result? Which is the result?

A: Find the critical points.

Q: How can I get the result? Which is the result?

A: The given function is,

Q: find the inverse of y from the function that is in the picture below

A: Giveninformation:The given function is

Q: graph quadratic function f(x) = -3x2- 12x -1

A: Consider the given equation

Q: b. Find the area of the region bounded by Y = xe ax and the x-axis on the interval 0,41, where a> 0....

A: Area of region which is bounded by f(x) and x-axis on [0,4] computed as follows.

Q: Which of the following limits could be evaluated using L'Hopital's Rule? Indicate all the apply. Sel...

A: (A) This limit was not in form 0/0 or infinity/infinity. So we can\'t apply L\'Hospital\'s rule for ...

Q: I got up to: 60-62t, then started doing 30 + the integral from t to 0 but I don’t know if I’m doi...

A: To find velocity we have to integrate a(t)= -62Answer: Velocity: v(t)=-62t+60

Q: lim x→3(2x3 -12x2 +5x+3)

A: We have to evaluate the limit as shown on white board.Let’s call (2x3 - 12x2 + 5x + 3) as f(x)

Q: Calculate the area, in square units, bounded by g(x)=4x+8 and f(x)=x2 +19x+62 over the interval [−9,...

A: We have to find area between f(x) and g(x) for given boundaries.f(x) and g(x) is given below:Graph ...

Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is inf...

A: The given function is f(x)=(7x2-70x)/(x2-100).The limit is to be calculated.

Q: Which of the following is the power series representation for p(x)? A. B. 8+k -3 -3 k k 1 k k 1 O C....

A: Refer to the question,To find the interval of convergence of the provided series,

Q: A hot-air balloon is 190 ftabove the ground when a motorcycle (traveling in a straight line on a h...

A: Let x be the horizontal distance from balloon to motorcycle, y be the vertical distance from the bal...

Q: How does the limiting behavior of solutions depend on the value of y(0)?

A: Given autonomus differential equation:Graph of function f is given.We need to show the the limiting ...

Q: Find the area of the region described. 18 The region bounded by y and y1 2 9+x The area of the regio...

A: y = 18 / (9 + x2)As a first step we need to find the points of intersection of the curve and the lin...

Q: Use any method to determine if the series converges or diverges. Give reasons for your answer.

A: The given series is

Q: How can I get the result? Which is the result?

A: Use online graphing calculator to graph of the function.

Q: Find the area, in square units, bounded by f(x)=3x+5 and g(x)=2x+1 over the interval [0,12]. Do not ...

A: Area of region between f(x) and g(x) over the interval [0,12] is computed as follows.

Transcribed Image Text

1. У (x2 + x3)4 9. У ln(x ln x) 1 + t 21. У 3x1n х 23, y = (1-x-1)- 25. sin(xy)-x2-y 27. y-logs 2x) 29. y--In sin x--sin-х 1. yan (4x) 33. yInsec 5x + tan 5x 35, y = cot(3x2 + 5) 37. y=sin(tan-/I +x3