4) Given the points A(1, 2, 3), B(5, 4, 3), and C(2, 1, 2), find angle C

Q: 9) Find the equation of the tangent to the curve y = 1+ Int and x=t+Int when t = 2.

A: Given problem:- Find the equation of the tangent to the curve y = 1 + lnt and x=t+Int when t = 2 .

Q: dx + dy = 0

A: The given differential equation is dy+dx=0  .............................. (1)

Q: 1. F(s) = 4s+2 s²+6s+34

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Q: 1) Find the radius of convergence and interval of convergence of the series. Show All Your Work.…

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Q: whose equation is y³ + 2xy + x² = 9 Using techniques we have learned in our course, perform the…

A: Given query is to find the derivative and equation of the tangent.

Q: 2 and x = 6. 4. Find the area bounded by the parabola y² = 4x and the line y = 2x - 4. ² and Find…

A: To find the area of region enclosed by given curves.

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Q: [x³√₁-x² x2

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Q: ) Find dw if w = xe³/², x = t², y = 1 — t, and z = dt 1 + 2t.

A: Topic:- application of derivatives

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Q: Find the area of the region bounded by the curve y=x^3-3x^2+3 and the x-axis.

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Q: The function fis defined as f(x) = -7 3x²+2 Find f(x-5). Write your answer without parentheses, and…

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Q: 4) A spherical scoop of vanilla ice cream sits on top of a waffle cone. The diameter of the ice…

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

Q: Water running out a conical funnel at the rate of 1 cu. in per second. If the radius of the base of…

A:

Q: af Find and ax af Jy f(x,y) = e⁹xy In (3y) 11 for the following function.

A: To find the partial derivative.

Q: lim X→+∞ 5 In³ x 2 X²

A: Let's evaluate limit.

Q: Sº₁ 1 2 x³ dx x²+x+1

A: Solution of given question is written in below steps.

Q: The general solution of y” + y = cos2 x

A:

Q: d. limx→→+∞⁰ 1000 In¹0 X 5 X

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Q: Find the general solution of differential equation, and when initial conditios are given, the…

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Q: Sx" xn sinx dx = −x” cosx+n n-1 cos x dx

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Q: 'SC x x x

A: ∫cot2(x)csc3(x) dxWe know that cot2(x)=csc2(x)-1=∫csc3(x)(csc2(x)-1)dx=∫(csc5(x)-csc3(x))dxWe know…

Q: f cot x dx Select one: a. In sina+c + c + c + c O b. In sec x oc. In csc r od. In cos x

A: cotx = cosx/sinx

Q: fx ax dx

A:

Q: Find the inverse of the function on the given domain. f(x) = (x-5)^2, [5,∞) f-1(x) = =

A:

Q: d. lim, In 1000 x ,5

A: Here, note that the function ln1000x grows asymptotically slower than the polynomial x5.

Q: Use the binomial theorem to expand the expression (u - 5v)¹

A:

Q: y=√√√x 0 Figure A 12. Consider the region in Figure A. Its area, using [f(x) - g(x)]dx, is

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Q: rcosh z Let F(x)= 1. Find F(0). 2. Find F'(x). √√√x+1 sin(1 t) dt.

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Q: x² dx -1 (2x²+2x+1)² sº₁

A: We have to evaluate the integral. ∫dxa2+x2=1atan-1(xa)+c

Q: 5. For z=x2siny show that 332 332 = дудхду дугдх

A: Topic = Derivative

Q: Let P be the point in 3-space with rectangular coordinates (√2, -√2, 2√3). (a) Cylindrical…

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Q: clnx Find the integral of ²x ye²dzdxdy

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Q: 7. y=4x²-5x is known to be the relationship in a curved archway. Determine the area under this…

A: Note that, the curve y=4x2-5x and x=5 and x=1 intersect at (5,75) & (1,-1) respectively.

Q: sec x = Let f(x) + x³e² - log₂ (5x + 1) + 1 x² √T Using the derivative rules learned in our course,…

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Q: Solve the following problems showing detailed solutions.Draw the complete figures for each question.…

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Q: Determine whether the following statements are True or False? y = f(x) 2 X (a) lim f(x) = 1 (b) lim…

A: Diagram is given. Determine whether the following statements are true or false

Q: 3 fin [ ха Txx² 2 - 1/2 to

A: To evaluate: ∫13lnx21+x212dx=∫1312lnx21+x2dx=12∫13ln x2-ln (1+x2)dx=12∫13(2ln x) dx-12∫13ln(1+x2)…

Q: 7. S√4x²+9dx

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Q: What is the solution of 5 |x - 2|dx

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Q: how did you get the final answer??

A: Let's find value of rate of change of slope with respect to x.

Q: 1. Evaluate the given integral Q. Q = $₁² [² (2² Your answer (x² - y) dy dx

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Q: Compute the derivative d/dx of the following functions: f(x) = x cos^2(4x)

A: The given function is: fx=xcos24x   As we know that; The Product rule: f·g'=f'·g+f·g' The Chain…

Q: lim x→>0¯ -3/x 2 x² e

A: This question is based on limits and L' hospital rule

Q: 5. Find the limit using any method of choice. x + 2 lim x-2 2x² x 10

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Q: 6. Find the intersection of the line I and the plane . 1:7=(4,-1,4) +t(5,-2,3) 2x+5y+z+2=0

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Q: Convert each pair of polar coordinates to rectangular coordinates 1. (3, 225 degrees

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: S 10dz 4z3-4z²+5z

A: To evaluate the given integral:

Q: A plane that passes through the points A(2,1,1) B(-1,-1,10) C(1.3.-4). Find a vector perpendicular…

A: