At which points on the curve y = 1 + 40x³ - 3x5 does the tangent line have the largest slope? (x, y) smaller x-value larger x-value (x, y) = = X X

Q: Change the Cartesian integral - ² dy dx into an equivalent polar integral. Then evaluate the polar…

A: To change the Cartesian integral ∫-55∫025-x2 dy dx into an equivalent polar integral. Then to…

Q: Find the derivative of the function. y = In(3x²-x) + 4x

A: y=ln3x2-x+4xd dx(lnx)=1xd dx(xn)=nxn-1

Q: Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and…

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Q: Learning Target INTI: I can correctly antidifferentiate basic functions and identify…

A: To find the general antiderivative of the given functions . The general antiderivative, also known…

Q: Find the absolute extrema of the function, if they exist, over the indicated interval. Also indicate…

A: Given function is:fx=-0.001x2+4.2x-80We have to find the absolute extrema of the function.

Q: S2x√6x- 6x-x² dx =

A: To find out the integration of the given expression.

Q: (a) Find the derivative of r(t) = (4 + t)i + tej + sin(5t) k. (b) Find the unit tangent vector at…

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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 the vectors T, N, and B at the given point. T = N = B = r(t) = (2 cos(t), 2 sin(t), 2…

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Q: Assuming that the equation below defines y as a differentiable function of x, find the value of…

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Q: A car rental agency has a budget of $3.2 million to purchase at most 120 new cars. The agency will…

A: We can solve it as given below

Q: Use spherical coordinates. Evaluate III z dv, where E lies between the spheres x² + y² + z² = 4 and…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = 8x², x = 1, and y = 0,…

A: V= 64π/5 For detail go through the solution

Q: Learning Target DA6: I can set up and use derivatives to solve applied optimization problems. A…

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Q: Use the washer method to determine the volume of the solid formed when the region bounded by y = x²,…

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Q: 16 cos 6nt dt = [

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Q: Evaluate the double integral. √ 9x (25+ y²)-¹dA; R R is the region in the first quadrant enclosed by…

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Q: Find an equation of the tangent line to the curve at the point (1, -1-). y = x³e-x y =

A: To Find: Tangent line to y=x3e-x, at point 1, 1e

Q: The derivative of a function is given f'(z) = (2²-21-8)g(x) for some unspecified function g such…

A: The first derivative of a function is given by fx = x2-2x-8gx,   gx>0 To determine: The point…

Q: a) f(t) = -1 0≤t0' c) f(t) = ) = 0 t0¹ e) f(t) = e³¹.cos(5t); f) f(t) = sen(t).u(t – 2π);

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Q: (b) Find parameters a and b such that the function jodonivi COS X f(x) = if if if x≤ 0 0 3 ax + b x²…

A: Given :

Q: A tank contains 500 gallons of salt-free water. A brine containing 0.25 lb of salt per gallon runs…

A: We solve the problem step by step

Q: 53 2 5 -4 -3 -2 -1 U V 2 3 Q Find the components of the addition of the two vectors u and v shown.

A: Ans= <0,-6>  For detail...go through the solution...I have solved step by step with the help…

Q: 15 sin ¹√2x dx = [

A:

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

A: Here we differentiate f(x) with respect to x until it becomes a constant

Q: Consider the following. x = ln(t), y = 2t, z = t², (0, 2, 1) Find the equation of the normal plane…

A:

Q: Find the volume of the solid obtained by 8x², rotating the region bounded by y = x = 1, x 2, and y =…

A: The given data is: y=8x2x=1x=2y=0

Q: If is differentiable, then the function. e + f(x) √√3 is differentiable.

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Q: Find the length of the curve. r(t) = cos(6t) i + sin(6t)j + 6 In(cos(t)) k, 0≤t≤ π 4

A: NOTE: Refresh your page if you can't see any equations. . the given curve is take derivative

Q: Given the vector u = (5, 3), find the magnitude and angle in which the vector points (measured…

A: u→=<5,3>

Q: volume of the solid formed when the region bounded by y = x and y = = x¹ is rotated about the…

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Q: Use the limit definition of partial derivatives to compute the partial derivative of the function…

A: f(x,y)=5-4x+6y-3x2y∂ ∂x(xn)=nxn-1∂ ∂x(constnat)=0

Q: 1. Find the derivative of the following function f(x) = 2√x-1

A: To find the derivative of the following function. fx=x2x-1

Q: Consider the following problem: a farmer with 650 feet of fencing wants to enclose a rectangular…

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Q: The region bounded by f(x) = −4x² + 16x + 84, x = 0, and y = 0 is rotated about the y-axis. Find the…

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Q: Find the dimensions of a rectangle (in m) with area 2,197 m² whose perimeter is as small as…

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Q: Find ax dy II of of ax dy f(x,y)=√√x² + 4y² || and (Type an exact answer, using radicals as needed.)…

A: f(x,y)=x2+4y2∂ ∂x(x)=12x∂ ∂x(xn)=nxn-1

Q: Show that the equationy/= -9y is satisfied for y = cos 30.

A: We are required to check that y=cos3θ satisfies the equation y''=-9y.

Q: 1. A tank initially holds 100 gal of brine containing 30 lb of dissolved salt. Fresh water flows…

A: (a) Let x(t) denote the amount of salt in the tank at time t. The rate of change of x is given…

Q: Find the absolute extrema of the function, if they exist, over the indicated interval. Also indicate…

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Q: Q18 Given s = 3a²c-2bc + 5abc² (a) (b) da dc || ||

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Q: 20,000e 1+ ķ xy-plane, where x and y are measured in centimeters, find the total population of…

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Q: Determine if Rolle's Theorem can be ap plied to r²+3r-18 x+9 f(x) = on the interval [-6, 3), and if…

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Q: Use differentials (or equivalently, a linear approximation) to approximate sin(56°) as follows: Let…

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Q: (a) Find the derivative. y = In(4x - dy dx (b) Find the derivative. y = ln ( 4x = dy dx 6) - 3 In(x)…

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Q: у-х-2 (1-1) х-у

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Q: Find the derivate of the function: a) f(t) = ₁ (t²-a) 8 F'(() = b) f(x) = 7 (x²³ - 7 x² + 4) 2 f'(x)…

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Q: f(x) = 3cos(x) - 4sin(x) f(x) = sec2(x) + pi cos(x) find the most general antiderivatives of the…

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Q: 2 Functions f and g are defined by f(x)=2(3+1)₁³ ,x+0 and 1 g(x)==-=-3₁ X≠3 respectively. (a) Find f…

A: The given functions are:f(x)=23+1x ;    x≠0       and        g(x)=1x-3 ;     x≠3

Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? *x+9² [1,…

A: