Q15 Find all non-zero derivatives of the following function: f(x) = 5x³ - 7x² + 9x - 1

Q: Consider the function f(x) = 4 2 x² x7 Let F(x) be the antiderivative of f(x) with F(1) = 0. Then…

A: Topic = Integration

Q: Find all Singular points of the given differential equation then classify as Irregular Singular…

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Q: Determine if Rolle's Theorem can be ap- plied to f(x) = x² + 3x - 18 x + 3 on the interval [-6, 3],…

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Q: A cylinder shaped can needs to be constructed to hold 500 cubic centimeters of soup. The material…

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Q: Assume that x and y are differentiable functions of t. For the following, find dx/dt given that x =…

A: given  x2+y2=136d dx(xn)=nxn-1d dx(constant)=0

Q: given by C(x) = -0.07x² + 75x. Find C(288) C(287) Interpret the result

A: we will find the required.

Q: Let f(x) = 7x sin(x) cos(x). Evaluate f'(x) at x = ³7. ƒ'( ³ ) =

A: I have appended the formula used in the solution part of the question

Q: The Second Gate As you move through the first gate, you can see another gate not far in front of…

A: Given: g(x) = x+5x2-25 The function does not exist when their denominator is zero. That is,…

Q: Find the arc length of the curve y = ln x - ²² on the interval [1,3].

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Q: Find the derivative of the function. y' = y = etan(e)

A: We use chain rule to find the derivative of the following function.  dftdθ=dfdt·dtdθ also use the…

Q: Find the derivative of the function. f(0) = cos(0²) f'(0) = =

A: Given   f(thita) = Cos(thita2)

Q: 6y' - 2y = xy¹, y (0) = -1

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Q: Question 16 ( Find the slope of this line. Part 2- Full solution problems. A line with positive…

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Q: The number of hits on a certain website​ (in thousands) is approximated by f(x)=30e^0.171x​, where…

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Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on…

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Q: 7. Evaluate the limit: lim . a. 0 b. 1 *--* C. d. T +00

A: Given: limx→ππ

Q: Answer the following questions. 1 A function f is given by f(x) = (x+1)|x+3| x+3 (a) Express f(x)…

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Q: Use double integration to find the volume of the solid bounded by the cylinder x² + y² = 9 and the…

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Q: The​ short-term demand for crude oil in Country A in 2008 can be approximated by q=f(p)=2,443,225p…

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Q: Question 21 Suppose that is differentiable function and f'(r) 2 2r-1 for all are R. If f(0) = 1,…

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Q: Q9 Given g(2) = 3 and g'(2) = 5. Evaluate f'(2) where f(x) = 5g(x) (a) 15 (b) 0 (c) 25 (d) 10

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Q: Q12 Construct the equation of the line passing through (0, -2) and (3,5).

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Q: Determine if the series n = 1 7+1 3+8" converges or diverges and choose the option that describes…

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Q: Find the derivate of the functions: a) f(x) = -3x²³ -4 sxt9 · f'(x) = (6) g (v) = 3 2√² +5V-9 g' (v)…

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Q: Find lim f(x) if, for all x > 1, x → 00 4 12ex - 24 4ex X 3√x √x-1

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Q: A water well has an 8-inch diameter and is 180 feet deep. The water is 15 feet from the top of the…

A: Given: Pumping the well dry which is 8- inch in a diameter 180 feet deep for which the water is 15…

Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.…

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Q: Write the equation of the tangent line to the curve at the given point. x² + y² + 6x - 3y + 7 = 0 at…

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Q: First, let me say that I appreciate all the valid help that I have been receiving because the step…

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Q: Express the integrand as a sum of partial fractions and then evaluate the integral. 10x² - 1 S 4 X X…

A: Given integral : ∫-10x2x4-1dx To find: The value of given integral using partial fraction. Let I =…

Q: Solve yy'= -(x+2),Y(0)=\

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Q: 5. Find the explicit solution of the given initial-value problem. dy e-x-ex dx 3+4y a) = y(0)=1 (b)…

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Q: The Sixth Gate After walking through the fifth gate, your computer informs you that more than half…

A: Given function f( t ) = 1a( 7t3 - 55t2 + 165 )40

Q: Using the ratio test to determine the convergence or divergence of the series series. O Convergent…

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Q: Use the Method of Undetermined Coefficients to find a particular solution to the equation and the…

A: The given differential equation: y''+3y'+2y=4x2-3ex ; y0=9, y'0=5

Q: Let C(x) represent the cost of producing x units of a particular commodity where C(10)=1000 and…

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Q: Determine the PDE of all surfaces cutting the family of cones given by x²+y²-a²z²=0

A: The family of cones given by the equation:   x^2 + y^2 - a^2*z^2 = 0

Q: Determine the derivative of each function f(x) = 3x³ + 2x² [K2] 1 b. f(x) = = = − 2x² [x2] x² c.…

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Q: 15 sin ¹√2x dx = [

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Q: In this problem, p is in dollars and q is the number of units. (a) Find the elasticity of the demand…

A: Given: p+8q=240

Q: A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles.…

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Q: For what values of p does the following series n=2 (Inn)p-2 n converge or diverge?

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Q: 3x³+1 f) lim x →∞0 4x³-1

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Q: Find the 4th order Taylor polynomial, T4, of the function f(x) = e³ centered at a = 1.

A: Given function:- fx=e3x

Q: = 4y cos(2x - 5y) at the point (5,2,8) Find the tangent plane to the equation z =

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Q: Determine an expression for the derivative of this function. (Do not simpli f(x) = (2x²-x)(√√x² - 1)

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Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to…

A: Given function: f(x) = 45x54 To find: Arc length of the given function f(x) over the interval [0,16]

Q: The cost of producing x bags of dog food is given by C(x) = 900+√700 + 50x²-x where 0≤x≤ 5000. Find…

A: The cost of producing x bags of dog food is given by Cx=900+700+50x2-x, where 0≤x≤5000. To find the…

Q: a) lim x-0 9+x-3 x

A: The solution is shown below-

Q: A ship sails on a heading of 240° for 80 km. It then goes on a heading of 140° for 110 km. Determine…

A: To solve the problem, we can use the law of cosines, which relates the lengths of the sides of a…