If you are going to evaluate the integral S V1 - 7w-dw using trigonometric substitution, the answer (Ø + sinØ cosØ) + C, then what is the equivalent to if w =sino

Q: Write a in the form a = a- T+ anN at the given value of t without finding T and N. r(t) = (t + 5)i +…

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Q: x2 dx is F(b) – F(a). where F(a) and F(b) are real numbers. What is the value of F(a)? The result of…

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Q: Consider the function on the interval (0, 27). f(x) = sin(x) cos(x) + 8 (a) Find the open…

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Q: 4. Given [2r + 5], if r2 I = -1 and at r = 2. If discontinuous, classify the type of a. Discuss the…

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Q: 7. dx = y(1+ y²)sec²x dy

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Q: Fird the area bounded by the curve: a) y=x° and y=2x43 a)Curve accurotely drown with important…

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Q: Find the sequence of partial sums S,, S2, S3, S4. and S5. 7 7 + 4 7 7 Σ = 7+ - 1 16 64 256 n = 1 S1…

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Q: The speed of a runner increased steadily during the first three seconds of a race. Her speed at…

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Q: The limit of a function is the value it approaches as the value of x approaches a certain value. a.…

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Q: x³ + 6x² + x+2 s ax + In[cx + 1}*(x² – x + 1)°| + fx-1 Tan-1. V3 The resulting integral of x³ +1 +…

A: use simple integration formula.

Q: s²+3 (s-3)(s+5)(s-1)²

A: Let  s2+3(s-3) (s+5) (s-1)2 = As-3+Bs+5+Cs-1+D(s-1)2

Q: tan (x) cos (x) 1 tan (x) +tan°(x) + C tan'(x)7tan?(x) +9]+ C 36 O 1 1 tan (x)-tan'(x) + C O…

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Q: /9– x² using Trigonometric Substitution what is dx ? onsider x2 3 sec e de P 3 cos e de O 3 sec e…

A: Topic:- application of integration

Q: Ssin(x)cos(2x)sin(3x) dx O sin(6x) sin(2x) , sin(2x)cos(4x) 24 8 8 + 4 sin(3x)cos(3x), sin(2x) +…

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Q: V x2 + 4x – 5 dy using Trigonometric Substitution find x- Consider x+2 O -2+3 sec e O 3 sec e sec e…

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Q: Using Integration By Parts, 2x² e3" dx = u v - |2x2 e3" dx = u v-, -Svau Find u v- Sv du · x3 e 3 dx…

A: Integral

Q: Given that A = (1,0,2) and B = (6, -2,3), solve for projąB.

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Q: Find the area of the region bounded by y = 4(x + 2), x = 2 and the x-axis. Answer:

A: Given query is to find the area bounded by the curves.

Q: Suppose that f(x) is a differentiable function satisfying the table below. 0 2 f(x) | 1| 2 | 12 | 7…

A: The objective of the question is showing that there exist at least one x=c for which f'(c)=5.

Q: dx -= In[F(x)]+C• What is f(3) For (x+x³) (x Tan-!x+1) 3 3 -1 3 6. + 3 + + +

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Q: Ssin(x)cos(2x)sin(3x) dx O sin(6x) sin(2x) , sin(2x)cos(4x) 24 + 8 8 sin(3x)cos(3x) , sin(2x)cos(2x)…

A: We need to evaluate integral.

Q: The function s(t) describes the motion of a particle along a line. s(t) = 12t – t2 (a) Find the…

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Q: Evaluate the definite integral: 1/5 dx 1-x2

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Q: Let f(x) = Vx +1. Calculate the difference quotient f(15 + h) - f(15). for h h = .1 h = .01 h 3= .01…

A: Given: f(x)=x+1 We have to find f(15+h)-f(15)h for h=0.1, 0.01, -0.01, -0.1 For h=0.1:…

Q: (2x + 4) + 1 (2x +4) +1 dx: x2 + 4x + 5 x2 + 2x- 10 2 2 2 Consider dx = x2 (x2 + 4x + 5) dx evaluate…

A: We can solve as follows

Q: (2х + 3у)dx + (у — х)dy —D 0

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Q: 9х2— 6 To evaluate dx using the method of partial fractions, the given integral can be rewritten as…

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Q: Find any critical numbers of the function. (Enter your answers as a comma-separated list.) g(x) = x6…

A: For critical numbers, Put g'(x) = 0 and solve for x.

Q: -. Evaluate f. F dr where F(x,y, z) = e²i + xzj+ (x + y)k and C is given by r(t) = t²i + t°j- tk, 0…

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Q: 1. Evaluate the following limits. 4x – 7 3x2 – 2r – 5 1 c. lim I-1- |I + ¤|

A: We put the limit .

Q: The velocity of an object is given by the following function defined on a specified interval.…

A: Given  v = 1(2t+2)m/s   for 0≤t≤8 ; n =4 Displacement = ∫081(2t+2)dx Number of subinterval = 4  h =…

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: Given,   r(t)=cos(πt)i-ln(t)j+t-16k

Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

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Q: 2x4 + 3x2 – 1 Rewrite dx as integral of sum of partial fractions. (x³ – 4x² + 5x)² C D E F + |dx x2…

A: First we factorise the denominator of the given function.Then write the given integral into integral…

Q: x2-y는 군.Give the spherical coordingtes.

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Q: 3r + cos r Use Squeeze Theorem to evaluate lim V1+r² – 5x°

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Q: In how many ways can the digits in the number 8,400,000 be arranged? ways (Type a whole number.)

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Q: Consider - x2 + 2x - 10 2 (2x + 4) + 1) dx · evaluate x² (x² + 4x+ 5) (2x+ 4) +1' dx - x2 + 4x +5 x2…

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Q: Sketch and determine the opening, vertex and focus of the parabola with an equation of y? - 8x + 16…

A: Follow the procedure given below.

Q: 1 Calculate the difference quotient for f(x) at a = 4. V2x + 5 (Express numbers in exact form. Use…

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Q: 1 A function f is given by f(x) = This function tak (x+ 4)2 f(x + h)-f(x) Find f(2), f(0), f(a), f(x…

A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…

Q: 9. Evaluate limf(x) = {"_ (x – 2; x 3 %3D x-3 а. 1 b. -4 с. 3 d. Does not exist 10. Evaluate limf…

A: Our Aim is to evaluate the limit of the expression given below:-limx→3 f(x)=x-2 ; x≤3-4;…

Q: 2x+11 3 1 dx evaluate Consider x² + x-6 dx- x+3 x-2 x+3 X-2 x-2 In +C |x+3 |(x-2)³| In x+3 |x+3 +C…

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Q: dx + (1 – x²)cot y dy = 0

A: Given problem :- dx + (1-x2 )cot(y) dy = 0 Find the general solution of given differential equation

Q: Use differentials to approximate the value of (3.01)2 + 2(0.99) – 3 in four decimal places.

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Q: Find the average rate of change of the function over the given interval. R(0) = 40 +1; [6,12] AR…

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Q: The slope of the tangent line at any point (x, y) on a curve is 2 If the point (9, 3) is on the…

A: Given that the slope of the tangent line at any point (x,y) on a curve is 2x. So, dydx=2x=2(x12)

Q: Evaluate the definite integral. sin(4t)dt

A: Here is the solution:

Q: Evaluate the integral 34 dr, by making the appropriate substitution: u = 5) da- 34 NOTE: Your answer…

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Q: r³ – 4x – 1 = 0 3 | Consider the implicit curve throughout this problem. Find dy/dx and use this to…

A: We can solve as follows