Differentiate the function. 4√x + 9x 7x² y' = y =

Q: b) (x + 2y - 3)dx + (2x + 4y - 9)dy = 0

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Q: bounded by the following curves: y = x³/2, y = 8, x = 0, y = 0. Find the volume of the solid…

A: Given ,       y = x32 ,  y=8  ,  x= 0 , y=0.  From Shell method-     Since the revolution is around…

Q: Differentiate the function. f'(v) = f(v) = 3 √√√v - 3vev V V

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Q: (a) Show that helpful). (b) Evaluate lim x-0 coth x dx = log sinh x| + c. (Hint: you may find the…

A: Integration using substitution

Q: Find the derivative of: 7 sin² ( – 2xº).

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Suppose u and v are functions of x that are differentiable at x=0 and that u(0) = - 4, u'(0) = - 6,…

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Q: Differentiate the function. g'(x) = g(x) 에너 1 VX +x

A: Given:g(x)=1x+x5

Q: 11) If the Taylor series of a function has the general expression xn f(x) = En=on! The corresponding…

A: To solve the following problem

Q: What is the median of the following list of numbers? [4, 12, 12 6, 10, 3] Number

A: given numbers  4,12,12,6,10,3first step is to find median is to sort our dataset from lowest to…

Q: Find the general solution to the system of ODE's x'= Ax, where -4-3 -1 - A =

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Q: enclosed

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Q: A particle that started at the origin and is moving along the x-axis has a velocity function given…

A: We need to find out the position of the particle after 39 seconds.

Q: 5) Find the divergence of (√x² + + z ²) kî + yî + zk)

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Q: Find the exact length of the curve. x = e² + e-t,_ y = 5 - 2t, 0 ≤t≤ 2

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Q: Determine the solution of the following differential equations. c) (D¹ + 2D6 + 7D5 + 14D4 + 8D³ +…

A: To determine the solution of the following differential equation.D7+2D6+7D5+14D4+8D3+16D3-16D-32y=0…

Q: The given point is on the curve. Find the lines that are (a) tangent and (b) normal to the curve at…

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Q: 1) The derivative of y = esec-12x, x > 0 is: a) 2e³ec-¹2x x√4x²-1 esec-12x b) x√4x²-1 C) x√16x²-1 d)…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Differentiate the function. g(t) = 9t + 8t² g'(t) = 9+16x X

A: given  g(t)=9t+8t2we know  dtndt=ntn-1g'(t)=d(g(t))dt

Q: Given the homogeneous differential equation, (4D³-3D+1)y=0. The roots of the auxiliary are Om = -1,2…

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Q: y = ln x, xy = 4, x = 1, x = 3

A: NOTE: Refresh your page if you can't see any equations. . here we have and the given interval is…

Q: Use integration by substitution to solve the integral below. Use Cfor the constant of integration.…

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Q: 6x. Using the formal limit definition of the derivative, prove that 3x² =

A: Using the formal limit definition of the derivative  we have to prove that derivative of 3x^2 is 6x.…

Q: a. Graph f(x) = . 2₁ b. Find lim f(x) and O A. ----X c. Does lim f(x) exist? If so, what is it? If…

A: Given function:- fx=1-x2x≠12x=1

Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

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Q: 13) y = [X²+2x-1'; dy = ? A) X+ Xt y B) 4y (x+1) (XH) (x²+2x-1) 3/2 D) - () ㅗ 2\x²2x-1

A: Question number 13 solved

Q: A circle with center O and passing through the origin is graphed below. What is the equation of…

A: From the figure center = ( -4 , 2 ) let r = radius

Q: Find the equation of the line through the y-intercept of y = x²¹ - 9x5 −7+ 9x² and the x-intercept…

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Q: Evaluate sin 5x cos 4x dx

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: (D7 + 2D6 + 7D5 + 14D4 + 8D³ + 16D² - 16D - 32) y = 0

A: The given differential equation D2+2D6+7D5+14D4+8D3+16D2-16D-32y=0. We have to find the general…

Q: Solve the equation dy 2y² – x² 3ry

A: GIVEN equation in this question dydx=(2y2-x2)(3xy)   SOLUTION- as we can see dydxis a homogeneous…

Q: Differentiate. f'(t) = f(t) = 8t t³t-1

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Q: The graph of f is shown below. Evaluate each integral by interpreting it in terms of areas. 1 So…

A: we need to find out the given integration by interpreting in the areas.

Q: The graph below shows the constant function y = g(t). -8 -7 -6 -5 -4 -3 -2 -1 4 -2 -3 -4 Answer: 8 +…

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Q: Find the critical point of the function f(x) = sin ¹2-72 in the interval 0 < z <1

A: Given query is to find critical points.

Q: Express the following sum in sigma notation. Use 1 as the lower limit of summation and k for the…

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Q: Two oil tankers crash in the Pacific Ocean. The spreading oil slick has a circular shape, and the…

A: We need to find radius and area.

Q: If lim X-5 f(x)-8 X-4 lim f(x)= X-5 = 1, find lim f(x). X-5 (Type an integer or a simplified frac

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

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Q: A force of 6 pounds is required to hold a spring stretched 0.6 feet beyond its natural length. How…

A: Given that, Force required = 6 pounds to hold spring streched 0.6 feet beyond its natural length. To…

Q: assume that Dr. Kim decides to purchase a car which is selling for $55,000 today. She needs to make…

A: Given query is to find monthly payment.

Q: (iii) Does n³ e" n=0 converge absolutely, converge conditionally, or diverge?

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Q: Given the following data, calculate b, of the quadratic New difference polynomial: f(x)=0 f(x₁) =…

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Q: Evaluate the integral. fact 6x + 3 x² 3 x5 5 x5 •3 2 x³ 3 - 6 x² co|800 x3 6 ln x + 3x 6x² 2 x3 3…

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Q: Use Calculus to find the behavior of g. g(x) = x³ - 3r²is restricted to the interval.x € [-1,4] 19.…

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Q: If f(x) x = √₁² (2²³ + Sº (t³ + 5t² + 2), dt then ƒ''(x) = =

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Q: Differentiate the function. F(t) = (3t - 5)² F'(t) =

A: Let's differentiate given function.

Q: Find the equation of the line through the point (-5, 4) and perpendicular to the line y = 2-5.…

A: In this question, we want to find a equation of the line perpendicular to the given line passing…

Q: Use mathematical induction to prove that the statement is true for every positive integer n. n(n +…

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Q: f(x) = (2x³ + 8), (1, 100)

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Q: Express the following limit as a definite integral. n 1 lim Σ -Ax where P is a partition of [2,4]…

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