If f(x) Files = Time left 0:5 sin²x and g(x) = 1 + cos²x, how are f'(x) and g'(x) related? Maximum file size: 20MB, maximum number of files :::

Q: √= - 4x + 43 x² 11x + 18 dx = +C

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Q: 1 The length of the curve y = x³ + x¹ from x = 3 to x = 4 is: a. b. C. d. 145 16 257 12 99 8 593 48

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Q: If 2x² + 3x + xy = 3 and y(3) = — 8, find y' (3) by implicit differentiatio

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Q: 7rer dr =

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Q: egrate the following by hand, shc 9 (a) 3 3 √x³ - 24+8) dx

A: We can solve this as follows:

Q: dr Let A be the area of a circle with radius r. If dt = 4, find dA dt when r = 5.

A: Area of a Circle , A = πr2 ; where, 'r' is the radius of the circle .

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Q: What is the derivative of k(y)=(6y^−1+3y^−2)(6y^−3+4y^−4)?

A: The given function is: k(y)=(6y-1+3y-2)(6y-3+4y-4) We have to find it's derivative with respect to…

Q: y 5 4 3 2 - 2 3 сл 1 2 В 5 6

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Q: 18. y = 3x + 2 20

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Q: Solve the following initial value problem for the unknown function y(x) a) y' = 2xy², y(1) == b) 2…

A: Topic:- application of integration

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A: Given :

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A: We have to find the equation of tangent line.

Q: Find the length of one turn of the helix given by r(t) == cos(t)i + sin(t)j + 1 1 99 25 -tk.

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Q: y=x4Inx

A: Topic = Derivative

Q: Determine whether the following relation represents y as a function of x. -6-5-4-3-2-1 y 7r 6 L 5 4…

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Q: 1 √3x²√x² + 1dx Calculate: -1

A: Concept: Integration: The term "integration" refers to the addition of discrete data. The integral…

Q: Given an, if limn→∞o an = 0 then the series 1 ∞ O diverges O converges O inconclusive O None of the…

A: series

Q: 10 5 f(x) 10 5 10 10 X

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Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an…

A: We need to find maxima and minima.

Q: -5 -4 -3 -2 -1 5 4 3+ 2+ 1+ -2- -3+ -4 -5+ ܐ 2 3 4 5

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Q: Find the average value of the given function from x=0 to x=1. Sketch graph of the function, roughly…

A: Average value of a function y=f(x)  from x=a to x=b is given by Aavg=1b-a∫x=ax=bf(x)dxsee below the…

Q: 5) Calculate the area of the region between the curves: y = 2 = x² and y = x²

A: We can find the area as below.

Q: Suppose that the position of a particle is given by s(t) = 4t³ + 5t +9. (a) Find the velocity at…

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Q: Find the indefinite integral and check your result by differentiation. (Use C for the constant of…

A: To give the solution with proper explanation for the given problem. To find the indefinite integral…

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Q: Calculate r' (t) and T(t), where T'(t) = ( T(t) = { r(t) = (8+t, (9+t), 2+2t). ).

A: Given vector function r(t)=8+t, -9-t, 2+2t

Q: 1₂ O 2² x² + x2° In | co - 3 2 O O None of the choices O +∞ dx In 2

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Q: Test 8 2k √k for convergence

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Q: The normal vector of x+2y-1-0 (0, 2) (2, -1) (1, 2) O (1, -1)

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Q: 8. Find the equation of the exponential function g(x). (No Decimals) Equation: -6 a

A: Solution ) from the graph  ( 0 , - 2) and ( 1 , 2 ) points are on the graph  Equation of exponential…

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A: Concept: Limit of a function: Think about the f function (x). X must have values ​​close to the…

Q: Explain how the fundamental theorem of calculus relates integrals and derivatives. Formats T B T U…

A: Fundamental theorem of calculus relates integrals and derivatives.

Q: -6-5-4-3-2-1 у 7г 6 4 3 2 1- -1 -2 -3 -4 -5 -6F 1 2 3 4 5 6

A: Range :- all the y value where function is defined

Q: (-5-x)²+2 if x #-6 Let f(x) = 2x + 14 if x = -6 Calculate the following limits. Enter "DNE" if the…

A: Given  f(x) = -5-x2+2if  x≠-62x+14if  x=-6

Q: Use Mathematical Induction to prove the following. 1 Show that 1+4+7++(3n − 2) + (3n − 2) = n(3n-¹),…

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: = Approximate the area under the curve y = x² from x with 6 subdivisions. 3 to 6 using a Right…

A: We have to approximate the area under the curve using Right Endpoint Approximation.

Q: tan' (2)

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Q: 3.2 Bus A leaves Worcester at 08:00 and travels north along the N1 at 50 km/h. Bus B leaves…

A: Given that The Bus A leaves at 8:00 with speed of 50 km/hand bus B leaves at 10:00 with 70 km/hSo,…

Q: फ 1/2 Determine the equation of the axis of the curve of the following trig function. ● a) y = -1 ©…

A: Please see the below picture for detailed solution.

Q: Compute the rotated area bounded by y = 2x, x = 2 and x-axis about x-axis

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Q: y=x4/5, x=0, y=4

A: Please see the below picture for detailed solution.

Q: -) 5cos(x +40°) - 3.6 = 0

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Q: A particle moves along the x-axis so that its position at time 0 ≤ t ≤ 18 is given b x(t), whose…

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Q: Find the following using the table below. X 1 2 3 4 2 f(x) 3 4 1 ƒ'(x) 2 1 4 3 g(x) 1 4 3 2 g'(x) 1…

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Q: Let R be the shaded region bounded between the curves y = x^1/3 (equivalently y^3= x) and 4y =…

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Q: Σ(-1)^+¹ Test k=1 1 for absolute/conditional convergence

A: The given series: ∑k=1∞-1k+11k5 .We need to test for absolute onvergence and conditional…

Q: Write the interval in set notation. [2, 6) {x | 2 < x ≤ 6} {x | 2 ≤ x < 6}   {x | 2 ≤ x ≤ 6} {x | 2…

A: Write the interval in set notation. [2, 6) {x | 2 &lt; x ≤ 6} {x | 2 ≤ x &lt; 6}   {x | 2 ≤ x ≤ 6}…

Q: Find the arc-length function s(t) for the line segment given by r(t) = (9 - 9t, 40t). s(t) = Write r…

A: Given :- r(t) = &lt;9-9t, 40t&gt; for arc length