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Q: d dx Prove that (csc(x)) = -csc(x) cot(x). d dx (csc(x)) = || = = d dx sin²(x) 1 sin(x) 1 -csc(x)…

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Q: x² + y² 2-100 and 6, find . dt X dx when y 8. (Enter your answers as a comma-separated list.) dt

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Q: diameter of each wheel of a bicycle is 27 inches.If you are traveling at a speed of 15 miles per…

A: Given query is to find the revolution of wheel per minute.

Q: Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

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Q: The position function of a particle is given by r(t) = (4t², (4t², 5t, t²- 1t). 1 At what time is…

A: rt=4t2, 5t, t2-1t To find the velocity, differentiate the position function with respect to t, we…

Q: How many possible real negative zeros are there for the function f(x) = 4x4 - 5x³+x² - 4x +1? A 0 B…

A: The given function is: fx=4x4-5x3+x2-4x+1 To find: How many possible real negative zeros are there…

Q: The so-called cuspidal cubic is given parametrically by the equations x = t³, y = t² Compute the arc…

A: It is given that x=t3y=t2

Q: (a) 3 inches is what part of a foot? (b) 3 inches is what part of a yard? (c) 2 dimes is what part…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: Let r(t) = (t², 1 — t, 4t). Calculate the derivative of r(t) · a(t) at t = 2, assuming that a(2) =…

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Q: What region R in the xy-plane maximizes the value of R (16-3x² - 2y²) dA? R is the set of points…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: f"(0) = sin 0 + cos 0, f(0) = 1, f'(0) = 4 f(0) = -sin (0) - cos(0) + (0) + 2 x

A: Given query is to find indicated function.

Q: 1 When is the velocity of the particle positive? When is it negative? When is the particle speeding…

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Q: Let f (x) = x² - 4x + 4 and consider the statements given below. Select all statements that are true…

A: Given:  fx=x2-4x+4 To Find: To determine the true statements for the given function for the interval…

Q: Write the exponential equation for the function going through the points (4,8) and (2,-6) and has a…

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Q: Video Example Evaluate = √√√elt². Solution e(x² + y² + z²j3/2 where B is the ball: B = = {(x, y, z)…

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Q: 10. (9x2 + y-1)-(4y - x) y' = 0, y(1) = 0

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Q: how are you getting pi. should it be pi/4 or is it because you are flipping 1/2 to 2/1. I am still…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: x+1 ƒ ( ² + ¹) + f(x) = x + 1 X find f(x)

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Q: Simplify the expression Show your work 2 T 6x3-17x2+20x-5 3x1 PENCIL THIN BLACK B

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Q: 16. Evaluate the limit for the graph: lim f(x). a. b. 3 | w 14 -1 4 -2 -2 0 +2 4 2 4 _0<x C. 0 els…

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Q: X y a= 1 884 2 1149 3 1618 4 5 2190 2962 6 3705 Use regression to find an exponential equation that…

A: Given Table : X Y 1 884 2 1149 3 1618 4 2190 5 2962 6 3705 .

Q: Let D be the region under the curve y = In √ and above the x-axis = e. Find the volume of the region…

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Q: Find the extreme values of f(x,y) = xy subject to the constraint x² + y² - 20 = 0. The extrema are…

A: To find the extreme values of fx, y=xy subject to the constraint  x2+y2-20=0.

Q: 5. Consider a unit vector u = (a,b). (a) How many unit vectors are orthogonal to u? (b) Explain a…

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Q: d the distance from the point (5,9,-6) to the plane - 3z = amon 18.

A: we will find the required.

Q: Solve the following initial value problem: dy t dt (3²,-²) y5 y(t)= | + = 0, y(1) = 1. 2y4 I

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Q: A cylindral drill with radius 5 cm is used to bore a hole through the center of a sphere with radius…

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Q: Solve the given differential equation. 3ydx - 3xdy + x* dx = 8dx The solution is (Type an equation.)

A: Given differential equation 3ydx - 3xdy + x4dx = 8dx

Q: І exta) (x+b) dx

A: integral

Q: The demand for a new computer game can be modeled by p(x) = 55-4 Inx, for 0≤x≤800, where p(x) is the…

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Q: x3 The function f is defined by f(x) = x-2 Find the x-coordinates of all local extreme values of f.

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Q: 6. Find the limit. Show your work algebraically. lim x48 (5 + 2/7)

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Q: is this fully simlified ?

A: Find the derivative of  f(x)=82x2+7

Q: x(t) = Find a plane containing the point (4,7,-4) and the line y(t) z(t) = = −4+t 2- 7t - 38t

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Q: (g) Graph the position, velocity, and acceleration functions for 0 ≤ t ≤ 6. O 30 20 -10 10 O 30 20…

A: Given that , ft=t3-9t2+24t

Q: Consider the four graphs shown below. For each graph, select Yes if satisfies the following…

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Q: 1. Find all critical numbers of the function f(x) = 1/3 sin (6x) -x, on the interval 0<x< Show all…

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Q: Find the critical points of the following function. f(x) = 9x 2 x² +81 Select the correct choice…

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Q: d dx [ 3+√√f(sin( sin(x)) cos(x) f' (sin(x)) 2√f(sin(x))

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Q: 1. For the function y = 2x²-3x use a simplified algebraic expression in terms of a and h to estimate…

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Q: 3x - 1 Let f(x)= X a. Make tables of values of f at values of x that approach x = 0 from above and…

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Q: Find an equation of the tangent plane to the surface at the g h(x, y) = In √√x² + y², (6, 8, In 10)

A: Given: h(x,y)=lnx2+y2  at (6,8, ln10) To find: The equation of the plane to the surface

Q: Water, at the rate of 12 cubic feet per minute, is pouring into a leaky container whose shape is a…

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Q: Calculate the iterated integral. 4 2 [*f* ( + ) ∞y dx dy

A: Integration

Q: c) Derivatives of trigonometric function and inverse trigonometric functions 6) Differen...... 7)…

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Q: Given that the acceleration vector is a(t) = (−1 cos (−1t))î + (−1 sin (−1t))ĵ + (−5t)k, the initial…

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Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: By using implicit differentiation to find an equation of the tangent line  to the curve at the given…

Q: (a) ( Find an equation of the sphere that passes through the point (-3, 3, -2) and centered at the…

A: We have to find the equation of the sphere that passes through the point (-3,3,-2) and centered at…

Q: Differentiate. Step 1 F(y) x) = (1/²2 - 11/2) (v + 8y²³) To find the derivative of the product F(y)…

A: The given data is:  Differentiate  Fy=1y2-4y4y+8y3