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Q: 12. Determine whether the following is true: (a) ≥3, EZ, 31(2²" - 1); n (n + 1)(2n +1) (b) 12+22+ 32…

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Q: d) Hence form a conjecture for the derivative of functions in the form y = (ax + b)². e) Prove your…

A: As you have mentioned I am answering Question (d) and Question (e)

Q: Find the equation of the tangent line to the curve y = 4x cos x at the point (, - 4). The equation…

A: We can answer the question in the following steps.

Q: d) f(a)= (2a-1)² 2a + 5a

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

Q: Introduction to Calculus in Economics (continued): In the previous Problem Set question, we started…

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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: 2 8. y' + ²y = -x²y² cos x

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Q: Sam makes $25.00 per hour. He gets paid time and a half for overtime. He gets paid every week. He…

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Q: 1. a) Copy the graph. YA 4 2 4-20 2 f(x) AR 2 4 x (g(x) b) Use the superposition principle to…

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Q: Can this also be solved using the mean value theorem? Thanks!

A: Given.

Q: 3. a. f(-2)= b. f(1) = c. lim f(x) =

A: Note :- This is multiple sub parts questions and according to our company guideline we can do…

Q: Find the unit tangent vector T(t) for r(t) = 4ti + 7t²j + 3tk. T(t) =

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Q: 5. (y4 - 2xy) dx + 3x² dy = 0; when x = 2, y = 1.

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Q: π 7. fz sin¹x cos¹ x dx

A: To evaluate the following integral by using Walli's formula.∫0π2 sin4 x cos4 x dx

Q: Use the binomial series to expand the function as a power series. V1-x 01-x-3-7--- (4n — 5) xn Σ - n…

A: The binomial series of (1+y)n is expressed as (1+y)n=1+ny+n(n-1)2!y2+n(n-1)(n-2)3!y3+......    where…

Q: Proceed to What I Know Chart for this part. 4) Activity 5: Check for Understanding (10 mins) ad of…

A: To verify if y=e-3x is a solution of given differential equation or not.

Q: ¹ // x² + y² + 2² dV, where E is the ball: x² + y² + z² ≤ 16. Use spherical coordinates to evaluate…

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Q: у=ех

A:

Q: 5. Determine whether the following are rational numbers: (a) 2² +27¹; (b) log₂ 3; (c) 2+√2. (d) If…

A: We have to find if the given numbers are rational or not.

Q: Use the graph of f (x): = Enter the exact answer. 1/1/00 below to find a number & such that |ƒ (x) -…

A: The objective is to find the value of delta.

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 .

Q: 8. A trapezoid has its vertices at (0,0),(a,h), (a + b1, h), (b2,0), with all the letters denoting…

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Q: Assume that the shape of the athlete's high-jump is parabolic. the function, in vertex form, where…

A: The axis of symmetry is t = 0.6 and the maximum height is 1.80 mhence the vertex is  (0.6, 1.80)

Q: 13. A radioactive isotope has half-life of 43 days. What percent of the original amount remains…

A: Topic:- application of algebra

Q: Sketch the region enclosed by y = 5x and y = 6x². Find the area of the region.

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Q: 2 1. The area of a rectangle is represented by the function A = 12x² + 48x + 48 cm² What is the…

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Q: (4) (b) 10tsin(5t²- n/4)dt (4) (c) S 12(x³ + 2)ex¹+8x dx

A: We have to evaluate the integrals.

Q: Find the sum by adding each term together. Use the summation capabilities of a graphing utility to…

A: We have to find the sum  ∑j=16 8j + 5.

Q: You are driving on a toll highway from King Road to Queen Road (a 50 km drive) in 25 minutes . Two…

A: Suppose, s(t) is the position function after t hours of time in km. Now, s(t) will be continuous and…

Q: Find the area under the curve y=sin2xcosx for the given limits; sketch the area. Hint: integral in a…

A: Topic:- application of integration

Q: The opposite vector of 10 N [S80°W] is 10 N [W10°S]. True False

A: Please see the below picture for detailed solution.

Q: y=x5, mn=-1/80

A: Given problem:- Find the equation of the line normal to a given curve y=x5 and having a given slope…

Q: 2. Captain Crunch wants his airplane to travel along a path that is [N60°W] with a groundspeed of…

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Q: 5. Which of the following functions grows the slowest as x goes to infinity?

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Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of f(x) = 4x + 4 between x =…

A: Given function, y=4x+4 x=6, x=8 First we draw the diagram

Q: Evaluate the triple integral W z dV where E is the solid bounded by the cylinder y² + z² = 100 and…

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Q: Imagine you want to enclose a field in the shape of a rectangle with a semicircle on one end. If you…

A: Imagine you want to enclose a field in the shape of a rectangle with a semicircle on one end. If you…

Q: Assume the coordinates are integers. Determine the coordinates of the point shown. (Type an ordered…

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Q: Let f(x) x³ + 6x² 36x +11. = (a) Use the definition of a derivative or the derivative rules to find…

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Q: Compute the first, second, and third derivatives of r(t) = 9ti + 5 In(t)j + 5e-3tk. first derivative…

A: As we know that; The Sum/Difference rule: f±g'=f'±g' The Power law: ddxxn=nxn-1 The Chain rule:…

Q: The annual rainfall in a certain country varies from 0 to 9 inches and is a random variable with…

A: It is given that the probability density function for the annual rainfall value is given by below…

Q: Determine the general solution of xdy + ydx = 0 A xy=c B) xy^2 = c y=c (D) X=C

A: Given Problem:- xdy+ydx=0 Find General equation  of given differential equation

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

A: We can solve this as follows:

Q: у 3 2 1 -1- -2 -3 1 2 3 4 5 6 X

A: Here is the solution:

Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

A: We have to find open intervals on which the graph is concave upward or concave downward

Q: Evaluate the limit of the given functions. 3x17x+ 20 lim. x44x² 25x+36 1. 2. lim t3 - 1 고 t-it-1

A: "According to the guidelines issued by the company we are supposed to answer only first three…

Q: Find the limit, if it exists. Ilm Submit Answer

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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) = <9-9t, 40t> for arc length

Q: 7. lim x-1x³ 2x²-x-3 + 2x² + 6x +5

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Q: A solution of the differential equation d²y dy +4- + 4y = 4e¯¹ dr2 da takes the value 1 when z = 0…

A: