Find the number or limit approached by the entire function as h approaches 0: 3h² a. lim h→0 h Find the equation of a line passing through (0,8) and having a slope of -4. Calculate the slope of the tangent to the curve of the following formula: y=-x² + 6x at x=7.

Q: If f(x) = x² - 2x +3 when x > 1, and f(x) = x when x ≤ 1, then f(2) + f(0) = 1 Do 3 -1 2

A: Given query is to find the value of the function.

Q: Find the area enclosed by the curves f(x) = 37 - x^2 and g(x) =x^2 The area (rounded to two decimal…

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Q: Find the equation on the ellipse that has its center at the origin and satisfies the conditions:…

A: We have to find the equation on the ellipse that has its center at the origin and satisfies the…

Q: Solve the problem. 15) Water is falling on a surface, wetting a circular area that is expanding at a…

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Q: Write an equation describing the relationship of the given variables. y varies inversely as the cube…

A: Given y varies inversly as the cube root of x when x = 64 , y = 4

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: Figure

Q: Solve for x in In(x+3)=5. Give an exact answer only. Write "no solution" if necessary. As always, be…

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Q: a(t) = t2 −4t + 6 , s(0) = 0 , s(1) = 20

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Q: Rewrite sin (a x + 11T 7) in terms of sina and cos x. Simplify your answer. 6 Enclose arguments of…

A: As we know that; The trigonometric identities: 1). sina+b=sinacosb+cosasinb 2). sinπ2-x=cosx 3).…

Q: Given vectors u = (-33, 6) and v = (-19,5), find vector u — v.

A: To find the vector difference

Q: 8. √(T-2) 0 - x) сos лx dx

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Q: a. Find an equation of the tangent line at x = a b. Use a graphing utility to graph the curve and…

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A: For xy-plane, z=0. For yz-plane, x=0. For xz-plane, y=0.

Q: The Maclaurin series for cosx is ...? O a) 1 + +2 +4 +6 2! 4! 6! ○ b) x - - 6 + .... 21 + 21 − 2 +…

A: f(x)=cosx The Maclaurin series of a function is given by :…

Q: Find the inverse of the given matrix. A = 1 -1 -1 0 2 1 0 = -6-7 Select the correct choice below…

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Q: The first 4 terms of the Maclaurin series for e -2x O a) 1 - 2x + x² - 4x³ Ob) 1 - 2x + 2x² – x³ -…

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Q: Suppose ƒ(x, y) = √√x + y² - 8. Find an equation for the level curve of f that passes through the…

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Q: Let g(x) be the inverse function to the differentiable function f(x). If f(0) = 1 and f'(0) = 3,…

A: Given: f(0)=1, f’(0)=3 and g(x) is the inverse of f(x) To find: g’(1)

Q: Solve the Bernoulli's equation, y dy = (x - y²) dx

A: Given that , ydy=x-y2dx Solve the Bernoulli's equation.

Q: Find a unit vector in the same direction as v = (-8,-6).

A: Given  v = <-8, -6> To find the unit vector in the same direction as a vector we divide it by…

Q: Which of these could not be a parametrisation of y² = 8x...? a) y = t, x = ² Ob) y = 2t, x = t - Oc)…

A: Solution )  y2 = 8x  a) When y = t  t2 = 8x  x = t2/ 8  ( correct )  b ) when y = 2t  ( 2t)2 = 8x…

Q: Find the angle between u = (4, -3) and v = (24, 10). Round your answer to the nearest tenth of a…

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Q: (a) find vectors 30 and +2 (b) find lu + 2√1

A: The answers are given below:

Q: how long would it take 20,000 to double if it earned 6.25 percent interest and was compounded…

A: Topic:- application of algebra

Q: Calculate the iterated integral. 13 3 2 LI (6x2y – 5x) dy dx /1

A: To evaluate the given double integral

Q: Find the arc length of the curve on the given interval. (Round your answer to three decimal places.)…

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Q: Which of the limits is equivalent to the following definite integral? Se e² dr Choose 1 answer: B…

A: To determine the limits which is equivalent to the following definite integral.∫03ex dx

Q: Write the sum without sigma notation and evaluate it. 3 π 25) Σ 4 sin k k=1

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Q: 1. (2x-y) dx +(4x+y-6)dy=0

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: f f(x) = V x + 1 , for x 2 -1, then for y 2 -1, fy2 + 2 y ) y + V2x+ 1 ) 1 - وكاد 1 ) V2x+y2

A: f(x)=x+1for f(y2+2y)  put x=y2+2y in f(x)

Q: Activity 3.4.2. A soup can in the shape of a right circular cylinder is to be made from two…

A: To determine the objective function

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A: To determine the next step of a maximization or minimization problem.

Q: Find the area of the shaded region. r² = sin(20) L

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Q: The value of 5 1 x² [³ - dx is

A: Given query is to find the value of integral.

Q: 2 2 Find ** (5x + 4y)5 drdy Question Help: Video Submit Question Jump to Answer

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Q: f(x) -4 -3 -2 10+ 8+ 6+ 4. 2 1 2 3 X Approximate the area between f(x) and the x-axis from x = -4 to…

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Q: Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

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Q: Suppose f(x, y) = 5y - 9x Find an equation for the level curve of f that passes through the point…

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Q: y dx + (x-xy+2) dy =0

A: given differential equation is  ydx+(x-xy+2)dy=0⇒dxdy=-x-xy+2y⇒dxdy+x1-yy=-2y which is linear…

Q: Use the graph of y=-x² + 3x + 10 to help you solve -x² + 3x + 10 ≤ 0 There is no work to be shown…

A: Consider the graph of the funtion

Q: 2. Suppose a thin wire with linear density 8(x) = ln(2x) lies between x = 1 and x = 3. Find the mass…

A: The given data is: The linear density of thin wire is δx=ln2x lies between x=1 and x=3 To find the…

Q: Find the average value fave of the function f on the given interval. f(0) = 5 sec²(0/4), [0, π] fave

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Q: 5. The function f(x) is a continuous, decreasing function on [0,10] with a critical point at (4,2).…

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Q: Obtain x²dx by integration.

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

Q: Find the numbers b such that the average value of f(x) = 3 + 8x − 6x2 on the interval [0, b] is…

A: formula for average value is  favg=1b-a∫abf(x)dx∫xndx=xn+1n+1+c

Q: Find an equation of the plane. The plane through the point (1, 8, 2) and with normal vector 5i + j -…

A: we have to find the plane equation which ,    passing through point P( 1, 8 ,2 )  and with normal…

Q: Given f(x, y) fz(x, y) = fy(x, y) · = fzz(x, y) = | fzy(x, y) = 2x³ 3x²y² + y^, find

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Q: 1 (6405 #3 p. 320) Let R denote the region bounded by the curve y = the y-axis, the z-axis, x² +1…

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Q: Given the following vectors, calculate −7u+4v U=(2,9),V=(-8,0)

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