12. Given the point ( 2, 1) on a tangent line to the curve ƒ(x) = x² − 2x + 5 find the point(s) where the tangent touches f(x).

Q: Determine the direction angles for the line with parametric equations x = 5 + 2t, y = 12 - 8t, and z…

A: Direction angle

Q: Find the volume bounded by: x² + y² + z = 16 and z-x² - y² = 8

A: Concept: If a solid S is bounded by a surface, as in rectangular coordinates,  z=f(r,θ) as well as…

Q: Determine whether the series Σ1 is convergent or divergent. If it is convergent, find its 3n 4-1…

A:

Q: For which of the series below the Integral Test can be used to determine whether the series is…

A:

Q: Find equation of plane which is containing Points A(2,1,1) and B(7,5,2) and normal to 2 x - 3y - 5z…

A:

Q: 5) a) Find the eccentricity, b) identify the conic, c) give an equation of the directrix & d) Sketch…

A: Concept: We know that a conic section is defined as the locus of a point that moves in such a way…

Q: Find the volume of the solid bounded by the elliptic paraboloid z = 2 + 5x² + 4y², the planes x = 4…

A:

Q: Solve the initial value problem y" + 4y′ − 32y = 0, y(0) = a, y′(0) = -80. Find a so that the…

A: We can solve this as follows:

Q: Find the first derivative of sin x y = In 1+2 In x x cot x-2(In x) cot x-2 x(1+2 In x) x cotx+2(In…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 06: b: dw (1) Find if dt w= w = tanx and x = 4t³ + t.

A:

Q: For the function f(x) = f'(x) = 0 x² 1+x find f''(x). Then find f''(0) and f''(8). 1

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Q: Find the exact length of the curve. x = et - 4t, y = 8et/2, 0≤t≤2

A:

Q: A conical vessel full of water is 16 ft across the top and 12 ft deep. Find the work required to…

A: Given: Volume of the conical vessel=13π r2h          where r= radius of vessel                    h=…

Q: f(x) = x² + 16 X 6 0<x

A:

Q: 1. If f(x) dx = 3, evaluate [[1 + 21(x)] dx using the properties of interga 2. If f(x) dx = -2 and…

A: As asked we can answer question no 1 and 4 as below.

Q: Determine whether the statement is true or false. True O False 00 [IF If ["f(x) dx and " g(x) dx are…

A: Convergence and Divergence. If the limit exists and is a finite number, we say the improper integral…

Q: Q3/A/Find the surface area generated by rotating the curve y = cos h(x) about x axis for 0≤x≤1

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

Q: dx 6) Stanh-¹ (in √x) x (1 - in ² √ x

A:

Q: Question 1. Let f(x, y) = eª + 2xy³ + x²y. Find the following: (a) ▼ f(x, y) (b) ▼ f(0, 1) (c)…

A: Note: As per our company guidelines we are supposed to answer the first three subparts of the…

Q: 10-8-8-4 191 6 30 O 45 X 10

A: Topic = Functions

Q: where does the function 1/sin(x) not exist? what happens if we try to calculate any of these values?

A: We have to find the values where function values doesn't exist.

Q: Given the function f(x) = x² + Draw a sketch of the graph of f. 16 X x>0

A:

Q: I Find the acute angle between the line joining A(1,2,3) and B(5,1,7) and the plane containing point…

A: Given that Line is passes through A(1,2,3) and B(5,1,7) And plane passes through C(1,0,2) D(5,1,6)…

Q: cel You are driving away from home. At noon, you are 212 miles away. Your velocity (miles per hour)…

A: This question is related to distance and speed, we will solve it using given information.

Q: dw 3. If w = f(x, y, z), g(x, y) = C₁, h(x, z) = C₂ find: dx constants. c1& c2 are

A:

Q: Consider the following equations. 3 y = 9- -1/2x², y = X₁ x = -2, x = 2 Sketch the region bounded by…

A: Here we have to find the area and the graph of the functions.

Q: Find the domain of the following function. 5 f(x) = 81-x² The domain is (Type your answer in…

A:

Q: QUESTION 16 hexagons can form a tiling of the plane. A. All OB. No C.Some

A: Option (C) is correct.See below the answer and explanation

Q: Write and evaluate the definite integral that represents the area of the surface generated by…

A:

Q: Question 2. Let f(x, y) = 5xy² + sin(x + y). Find the following: (a) The gradient of f(x, y). (b)…

A: as per company guidelines we solve only first three subparts when multiple parts question being…

Q: For the following function find (a) f(4), (b) í (b) f 2 f(x) = 4x² - 24x + 21 (a) Find the value of…

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Q: Find the first derivative of y = Arc tan √x² −1+ Arc csc x 2 O 2 O 0 2 Ox√²+1

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: alla Find xy² R2² -dA, R= [0, 4] × [ - 2,2] x² +1

A:

Q: Starting at age 30, you deposit $2000 a year into an IRA account for retirement. Treat the yearly…

A: We have to find the value of IRA.

Q: answer

A: We will find the anti derivative.

Q: A manufacturer of shirts determines that her fixed costs will be 500 dollars plus 9 dollars for each…

A: Calculation of above requirement are as follows.

Q: dy Find by implicit differentiation. Then find the slope of the graph at the given point. dx 3x³y =…

A: " According to the guidelines issued by the company we are supposed to answer only one question.…

Q: Find an equation for the tangent plane to the surface z + 1 = xy² cos(z) at the point (1, 1, 0)

A: Solve by eq

Q: The interest on an account increases exponentially. If an initial investment of $4000 earns $1300 in…

A:

Q: What is the average value of f(x) between x = 1 and x = 5 forf (x) = 2.t? 32 O 31 O 10.82 9.28

A: Average Value of f(x) between x=a and x=b , favg= 1b-a∫ab f(x) dx

Q: A firecracker shot straight up in the air has a height s, in metres, at time t, in seconds, given by…

A: Let xt be the curve followed by the object, then the formula for finding the instantaneous velocity…

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: We have to sketch the graph of given function.

Q: A movie stuntman receives an annual salary of $110,000, but becomes a quadriplegic after jumping…

A:

Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) (x(t), y(t),…

A:

Q: Find a, b, c, and d such that the cubic function f(x) = ax3 + bx2 + cx + d satisfies the given…

A:

Q: Determine whether the series sum. 1 12 16 3 4 The series is divergent. n=1 4n-1 is convergent or…

A:

Q: Starting at age 35, you deposit $2000 a year into an IRA account for retirement. Treat the yearly…

A:

Q: √√³0 3 dA over the region R = {(x, y) | 0 ≤ x ≤ 4,0 ≤ y ≤ 2} by identifying it as the volume of R…

A:

Q: y = 2 sin(x), y = ex, x = 0, X = K|N 2

A: The region bounded by the curves,  y=2 sin(x), y=ex, x=0, x=π2

Q: Find the derivative of the function. f(x): = sin ¹(6x) f'(x) = | −6 cot ( 6x)csc(6x)|× Need Help?…

A: