Prove the following by Mathematical Induction 1. 1/1(2) + 1/2(3) + 1/3(4) +...

Q: Determinant of n x n Matrices. Solve for the determinant of the following matrices using (a)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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A: The objective of the question is evaluate the indefinite and definite integral.

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Q: А. f(x) 3D Vx + 1; а %— 6 if x > 1 if x < 1 a = 2 С. f(*) — 13х + 1l; а %—-+ a = (3х — 2 В. f (*) —…

A: Only Function given in (C) is continuous at that point but not differentiable at that point. For…

Q: Let f(x, y) = 2x2y + 3xy. Use the (limit) definition of partials derivatives to show that fx(x, y) =…

A: This question is related to Partial derivatives, we will solve it using given information.

Q: 12sin3xcos7x dx

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Q: Find the derivative of the function. 3 In (x +8) 5-5x O A. dy %3D dx (x + 8)(5 – 5x)? О в. dy 15 -…

A: Given query is to find the derivative of the expression.

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A: The given function,       fx=x+10x2+3

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Q: Find the equation to the line below. y = [?]x Enter + or - to indicate if your answer is positive or…

A: As we know that; The equation of the line when it passes through the two points x1,y1 &amp; x2,y2.…

Q: Find the area of the shaded region. y 14 y= 7x- x² 12 10 (5, 10) 6 4 2 y=2 x 2 4 6 8 CO

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Q: 4. (3a* +23a +10a -21a+58)÷(a+7)

A: Given that,    3a4+23a3+10a2-21a+58÷a+7

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Q: sin' xcos³x dx 3

A: Given: I=∫sin7xcos3xdx   As we know that; The trigonometric identity; sin2x+cos2x=1 The Power rule:…

Q: 5. Determine the vertical and horizontal components of each force. a. 810 N at an inclination of 75°…

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Q: Evaluate the integral cos3 x + sin? х+1 dx cos² x (sin² x + 1)

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Q: 2. Write the given (total) area as an integral. a. The area above the x- axis and below y = 4-x2 NI…

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Q: 9. Suppose that the demand equation for a monopolist is p = 100 – 0.01.x and the cost function is…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: • Find the volume of a solid generated by rotating: Complete and chronological solution: 1. Region…

A: Solution is given below:

Q: The total cost to produce x handcrafted wagons is C(x)= 80 +3x -x +5x°. Find the marginal cost when…

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A: Trigonometric substitution in indefinite Integration

Q: 1. Show that cosh 4x = 8cosh“x - 8cosh? x + 1 .

A: Given problem:- Show that cosh(4x) = 8cosh4x - 8cosh2x + 1

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Q: Set up the definite integral required to find the area of the region between the graph of y = 15x +…

A: here i am giving my handwritten solution.

Q: Let u(æ) = sin(x) and v() = a = 18 and f(x) (*)a u (2) -| v (2) = u'v – uv f'

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Q: Sketch the following points in space three, A (4,5,3); B (1,7,4) and C (2,4,6). Prove that point A,…

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Q: Given f(x, y) = e"v, find

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Q: 30. The number of floats in the last Panagbenga Festival is about 50. This year, it is expected that…

A: Use permutations method nPr=n!/(n-r)!

Q: Evaluate the integral (Partial Fraction Decomposition) xdx J (x² + 2)(x² + 1)2

A: ∫xdx(x2+2)(x2+1)2Substitute u=x22→dudx=x→dx=1xdu=12∫1(u+1)(2u+1)2duPerform partial fraction…

Q: The sales of a new high-tech item (in thousands) are given by S(t) = 94 - 90 e-0.2t where t…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Sketch the region enclosed by x + y = 42 and x + y = 0. a) Favoring convenience, should you…

A: Given; x+y^2=42 , x+y=0

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Q: Evaluate the definite integral. 1 |(7x2 - 4x +6) dx

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Q: Evaluate the integral sec² x tan? x + sec x (sec² x + 1) dx 2 sec x tan x (sec2 x + 1)

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Q: A. For the following power series determine the interval and radius of n+1 convergence.a (x - 2)"…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Find the maximum and minimum values of the function g(0) = 30 – 8 sin(0) on the interval [0, T]…

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Q: IV. On Circular Permutation In how many ways can eight people be seated at a round table? . In how…

A: Note that, in a Circular fashion we can arrange n elements in (n-1)! ways.

Q: Evaluate the integral (Trigonometric Substitution) |(a?x* – x®)&dx 6. x³)Zdx

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A: Given problem:- ∫ 3t3(t2+4)5 dt

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A: Solved below.

Q: Find the equation of the tangent line to the curve y = 4sec z – 8 cos z at the point 4). The…

A: We can sole this as follows:

Q: 5. Given R(t)= 2 sin ti+5 cos tj+tk. Find T (t) and N(t) of the mov by the given vector.

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Q: dx .4

A: we have to find out the integral

Q: 3. A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a…

A: As per our guideline we are supposed to be answer only one question you can repost other question in…

Q: -5 4 -3 -2 /-1 1 2 3 4 The function graphed above is: Increasing on the interval(s) Decreasing on…

A: topic- increasing and decreasing intervals of function