Question 1. (5 marks) Find the distance between the point A = (2,2,3) and the line L : x = -1-4t, y = 5+ 4t, z = -1- 2t.

Q: H.W: Estimate the root of the equation for the following equation using Secant Method: 1. x³-5x = 3…

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…

Q: Find a power series representation for the function. f(x) = x2 tan-1(x3) f(x) = Σ n = 0 Determine…

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Q: Find all solutions of the equation in the interval [0, 27). 2 cos 0+1=0 Write your answer in radians…

A: Given:   2cosθ+1=0   2cosθ+1-1=0-1             {subtract 1 from both sides}   2cosθ=-1   2cosθ2=-12…

Q: 1)

A: Solution ) 1) in the first graph   We see that  In every value of x , y value is constant which is 2…

Q: Find the angle that maximizes the area of an isosceles triangle with legs of length / = 8. (Use…

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Q: 1. Find the area of the region bounded by the curve y=- 1+x² 2x² and the lines y = 0, y = x,x= 2.

A: First we draw the graph,

Q: 4. Letf(x)=x22/5 - 19x². Determine the largest n for which fis n-times continuously differentiable.

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Q: = C₁e^ + c₂e^, (-∞0, ∞0); y" - y = 0, y(0) = 0, y'(0) = 5 ex- 25e-x X

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Q: Find an equation for the line below. -6 -2 5

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Q: 1/2 cos ¹ x dx

A: The integration of the integral is cos-1x, limit from 0 to 1/2.

Q: Q5: (A): Finding a curve whose slope at the point (x, y)is 3x² if the curve is required to pass…

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Q: Qs/ Find the ave of the region R enclosed by the parabola x = - y²) and the line Y. X +2

A: find the shaded area

Q: Evaluate the double integral: S² SATI 1/3 x² +1 (Hint: Change the order of integration to dy dr.) dr…

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Q: Calculus Use partial fractions to evaluate the integral 1²-21+3 12² (x − 3)(x² + 9) dx.

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Q: (3+h)¹-81 The following limit limh→0 h represents the derivative of some function f at some number…

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Q: The radius r and height h of a cylinder are changing with time. At the instant in question, r = 4…

A: Given problem:- The radius r and height h of a cylinder are changing with time. At the instant in…

Q: 1 1 x² + 1 2 dx

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Q: 3. Set-up the iterated double integral in polar coordinates that gives the volume of the solid…

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Q: ACME Thingamjigs ltd. produces two types of thingamajigs, Type 1 and Type 2. The demand for…

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Q: Consider the right triangle shown below where a = 7.02, b = 11.18, and c = 13.2. Note that and are…

A: Given, a=7.02,b=11.18c=13.2

Q: The toll T charged for driving on a certain stretch of a toll road is $2 except during rush hours…

A: According to the guidelines, we are answering first three subparts. Please repost the remaining.…

Q: Find the area of the surface obtained by rotating the curve from x = = 0 to x 5 about the y-axis. =…

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Q: 3 [₁³e- t³e-2t dt

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Q: ntegral sydx 2. ] [ -1-1 (x + y + 1)dxdy

A: As per our norms we have to write one question at a time kindly repost remaining questions

Q: C 10 A 3 2- 1 1 2 3 4 To find the blue shaded area above, we would calculate: [1(x)d f(x)dx = area…

A: As shown in diagram, lower limit is 1 and upper limit is 2, Therefore a=1b=2

Q: Evaluate the following. Show your complete solution. 1. S. 2³ dz ₂ S. 39 dy 3/4 2. 6 S. 3. dx S.…

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Q: 5. By considering the derivative of the function f : [-1,-1] → R defined by f(x) = show that f-¹…

A: Concept: inverse function: An inverse function, sometimes known as an anti function, is a function…

Q: The director of the school play has to assign 5 lead roles. If the roles are being chosen from a…

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Q: π/2 cos² x dx

A: This question can be solved using the concept of properties of definite integrals.

Q: x² −x+3 Can the Fundamental Theorem of Calculus be used to find 52 dx? ○ No, f(x) = x²-x+3 3√x is…

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Q: The diagram below shows a right triangle that has side lengths of 7.75 and 1.98 cm and interior…

A: The tangent of an angle is the ratio of the length of the opposite side to the length of the…

Q: Find the arc length of the curve x = -2y³/2 from y = 0 to y = 10. Length =

A: Solve the following

Q: The illustration below shows the graph of y as a function of x. Determine the kind of function…

A: Explanation of the answer is as follows

Q: First find the equation of a plane through the point (4, 2, 1) with normal vector = 3i - 2j+ 4k.…

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Q: a.) Show that an is a perfect square where the sequence {an) is defined recursively by an+2 =…

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Q: d/dx [x/(x^2 + y^2) ] = * O [(y^2 + x^2)/(x^2 + y^2)^2 ] O -[(y^2 +x^2)/(x^2 + y^2)^2 ]…

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Q: sec¹ x dx

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Q: 13. y = x², y = 0, x= 1; about the y-axis

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Q: Q2: (A) Show that if y=csc(u), then dy du -csc(u) cot(u) dx dx

A: follow next step

Q: [x² x² tan-¹ x dx

A: We will use integration by parts to solve this question.

Q: Solve the compound inequality. 3x+2 ≤ 10 or 2x+1 <-1 Write the solution in interval notation. If…

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Q: √tanx secox dx

A: We know that integration of xn is xn+1/n+1.   Here i attached the solution of this question.

Q: For the function z = 3x³5x³y² + 4y³, Show that Zyx = Zxy

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Q: 1 (2m-3)√4m (m-3) dm

A: Given

Q: Sketch the graph of a function f that is defined on R and continuous except for the stated…

A: A function fx is continuous at x=a if limx→a-f(x)=limx→a+f(x)=f(x)

Q: find the solution of the problem with given initial value, using homogeneous equations with constant…

A: In this question, we want to find the solution of the given IVP using homogeneous equations with…

Q: Q2) Show that these statements constitute a valid argument, use Truth Tree: a) ~(pVg) = ^p^^q b)…

A: This is a problem related to mathematical logic parts. Based on the general formula and concept we…

Q: Q1: If the function f(x) define as f: R →R such that f(x)= (x+1, x>2 x²-1, x≤2 Show that the…

A: Solution is given below:

Q: Evaluate: lim (x² + €¯²) (x²¹ cscx) I→0+

A: We will evaluate the given expression using DL hospital rule.

Q: (c) an = (-1)". 2n n!

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