Consider the helical segment of the following figure defined by the parametric equations x = ncos(1), y = Tsin(t) and z = t for 0

Q: Find the equation of the tangent line to the curve y = 6 sec z – 12 cos z at the point 6). The…

A: y'=secx-12cosx' =secxtanx+12sinx Slope = secπ3tanπ3+12sinπ3=83. So, we have possible equation of…

Q: Application

A: We will find the area with the largest dimensions.

Q: Assignment: Determine the derivative of the ff. functions. 1. y = 8x5 - 2021, 5th derivative

A:

Q: Graphs of f(x) (solid) and g(x) (dashed) are given below. Use them to find the following ves. Show…

A: The given graph of functions is as follows:

Q: Find the average value of f(x) = over the interval [1, 3]. %3D (2x² + 3)²

A: The objective of the question is evaluate the average value of the given function.

Q: Find the equation of the tangent line to the curve y = 6 sec a – 12 cos a at the point (, 6).…

A: To find the equation of tangent for the given function.

Q: II. Find the first derivative of the given function. tan 2x 6. у %3 1-cot 2x

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Q: 4 s cot?x csc'x dx CSC X

A:

Q: Evaluate the integral: 5x/8x² – 1 dx - 5 (8x2 – 1)- + C (8a? – 1)-+ C (822 – 1) + C -(8x2 – 1) + C 8…

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Q: Test the series for convergence or divergence. TT 17. 2 (-1)" sin - n=1 n

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Q: A farmer plans to enclose a rectangular pasture adjacent to a river (see figure). The pasture must…

A: topic- application of derivatives

Q: Given that f(2) = 6, f‘(2) = − 1/2 and f‘’(2) = 10, what is the most accurate Taylor polynomial…

A: f(x) =f0(2)0!(x-2)0+f1(2)1!(x-2)1        + f2(2)2!(x-2)2f(x) =f(2)+f1(2)(x-2) + f2(2)2(x-2)2

Q: If, when the temperature of the air is 290 Kelvin, a certain substance cools from 370 Kelvin to 330…

A: Given problem:- If, when the temperature of the air is 290 Kelvin, a certain substance cools from…

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -10, 5), and the plane given…

A:

Q: Evaluate the definite integral. Use a graphing utility to verify your result. 8. -Ix - 5|) dx

A: topic - integration

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

A: Here we have to find the volume generated by rotating the region bounded by the given curve about…

Q: Consider the following. u = (-9, -3, -7), v = (-4, -5, –1) (a) Find the projection of u onto v. (b)…

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Q: The height (in feet) of a rocket launched from the ground is given by the function ft) = -162 +…

A: The given function is  f(t)=-16t2+160t.

Q: Given that lim f(x) = 2 and that lim f(x)= -2, does lim f(x) exist, and if so, what is its x→-2…

A:

Q: logarithm

A: We will expand the logarithms.

Q: Find the dimensions of the rectangle of maximum area that can be inscribed in a right triangle with…

A: A rectangle is inscribed in a right triangle. The base of the triangle is a=12 inches and height of…

Q: (ii) Find the following indefinite integrals: 1 (a) dx (b) dx 5 - x* xe* ! dx (c)

A: A)I=∫ 1x3+1x3 dxI=∫ x-3 dx + ∫ x-13 dxI=x-3+1-3+1 +x-13+1-13+1 +CI=-12x2+3 x232 +CI=32x23 -12x2+C

Q: Find the point (xo, yo) on the graph of y = x + 9x2 + 3x - 4, at which the slope of the tangent line…

A:

Q: 1which Statement is true? A incn) absolutely. Sinc) converges combergeng because converges lim.…

A:

Q: What is the equation of the vertical asymptote of f(x) = tan x where 0 < x < n

A: First draw the graph and get the vertical asymptot.

Q: Evaluate V (6x + vy) ds where C is given in the accompanying figure. (1,1) 1- y=x y=x2 (0,0 ds =…

A: We need to evaluate integral.

Q: 1. Evaluate the following integrals: g) dx sin-1 x V1 – x² h) . cos(sec-1 x) dx xVx² – 1 2 2/V3

A:

Q: 1. y = 8x5 - 2021, 5th derivative 2. y = x5 - 3x4 + 6x³ - 9x² + 12x - 15, 4th derivative 3. y = 2x2…

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

Q: 3-4 3. - find A-! L i As

A: Given query is to find the inverse matrix.

Q: 2. Find the derivatives of the following equations: y = sin¬'(1 – t) y = csc-(x/2) y = In(tan¬1 x) y…

A:

Q: Determine the equation of the line that is tangent to y = elan (2x) at x = 8

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Q: V9-4x2 The integral of the given function dx is x2 -19-4x2 а. 2x ArcsinA + C -V9-4x b. 2x - 2Arcsin…

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Q: A closed rectangular box is to have a square base and a volume of 40 ft3. y Letting x denote the…

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Q: 6k k! x Find the radius of convergence of2 k=1 (3k) k = 1 The radius of convergence is (Type an…

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Q: Find the exact value of the expression. co(sn-() - cot-(V3)) 2 Need Help? Read It

A:

Q: A 13 ft ladder is leaning against a house. The ladder slides down the wall at a rate of 3ft/min. a)…

A: We have to use differentiation to solve the problem

Q: 20. What is the equation of the tangent line of f(x) = Vx = 4? A. x - 4y + 4 = 0 B. x + 4y -4 = 0…

A:

Q: 1. S sin sin de

A: ∫sinx5sinx2dx Use the identitysinAsinB=12(cos(A-B)-cos(A+B))…

Q: 10. What value of k makes the function {2x - (4(x + k) if x > 2 if x <2 f(x) continuous at x = 2? А.…

A:

Q: Find the average value of f(x) = over the interval [2, 4]. (3x + 1)2

A: Given problem:- Find the average value of f(x) = x/((3x2 + 1)2 ) over the interval [2, 4].

Q: Tutorial Exercise Find two numbers whose difference is 186 and whose product is a minimum. Part 1 of…

A: Let's find.

Q: The public health authorities of a small town have divided the population into three categories:…

A: Note: There are multiple sub questions. No specific question has been asked. So, We will solve the…

Q: -1 sec vo) do

A: We will use substitute method to solve the integral.

Q: Determine if the relation defines y as a ône-to

A: The given graph is: To determine if it is one-to-one.

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

A: Let,  f(x,y,z)=x2+y2+z2 &amp; g(x,y,z)=x+y+x-27=0...(1) Let, λ be a Lagrange's multiplier such that:…

Q: -. n the base b of a triangle is increasing at a rate of 3 inches per minute while its height h is…

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Q: 5 and a is an angle in quadrant 1. 13 Suppose that a and B are angles given as follows: sin a cos B…

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Q: (3k + 8)! Consider the series> ar k3k k-1 k-1 a) What is ak+1? ak+1 = aktl ? b) What is ak ak-1/ak =…

A: The given series,     ∑k=1∞ak=∑k=1∞3k+8!k3k

Q: Determine whether the two functions are inverses. -5 -5-2x w (x) = and z (x) x+2 dz(x) = O The two…

A: Given: w(x)=-5/(x+2) and z(x)=(-5-2x) /x.

Q: Sondere ebch exprO sSn to G sngle logarithm 3. 2. 3. + log qfu + lay a to 3.

A: