Provide the complete solution (typewritten if possible) for the item below. Consider the plane π : x − 2y + 3z − 1 = 0 and the line l : x = (1 − y)/2 = z + 1. Find the point-normal equation of the plane perpendicular to π and containing l.

Q: hat is the average rate of change of f(x) = ln(x+4)/2x+1 over each interval? Give the answer…

A: Given: f(x) = ln(x+4)/2x+1 (a) [-1, 8] (b) 3.45<=x<=5.25

Q: 4. Evaluate the line integral f x siny dx + y dy, where C is the arc of r(t) = ti + t²j from point…

A: Line integral

Q: Praw the curve r= 4 + 8 case and find the area outside the inner loop of the curve

A: Given: r=4+8cosθ

Q: In a town of population 12,000 the rate of growth of a flu epidemic is jointly proportional to the…

A:

Q: When a consumer has quantities, ₁ and ₂, of apples and oranges respectively, his utility is given by…

A: Concept: Lagrangian function : The initial problem is reformulated as a result of the link between…

Q: 1. √ 2x log 2x dx

A: The objective of the question is evaluate the indefinite integral. Note -  As per our guidelines we…

Q: 6. If a = 2, b = 2√√3, y = 30°, solve for c and 3.

A: In a triangle, the given measures are a=2, b=23, γ=30°

Q: 1. Explain two different ways to solve for the derivative of s(0) = 200sin cos

A: Topic = Derivative

Q: Two fire-lookout stations are 14 miles apart, with station B directly east of station A. Both…

A:

Q: 8 №₁ 4-x² x+4.x² dx

A:

Q: Consider the plane π : x − 2y + 3z − 1 = 0 and the line l : x = (1 − y)/2 = z + 1.      1.      Find…

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Q: Find the volume of the solid obtained by rotating the region enclosed by the curves y = 1 and y =…

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Q: O

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Q: Solve the area bounded by the curve y = 4x-x and the lines x=-2 and y = 4. 12) Sketch of the curves:…

A: The given problem is solved below in detail.

Q: Find the Fourier series for the following functions: f(t) = |sin t], -1 < t < n and The function is…

A: Solution is given below:

Q: The base of the solid is the triangle enclosed by x + y = 11, the x-axis, and the y-axis. The cross…

A:

Q: dr 4+x² S Choices: tan ¹(x + 2) + C 1 In x² + 4 +C In x + 2+ C 1 tan 2 1 ¹ 1/2 + +C

A:

Q: Suppose that h(x) = f(x) g(x) and that we know the following f'(3) = -1, g(3) = 2, & g'(3) = -5.…

A: Topic:- calculus

Q: 1-y 2 Consider the plane π : x - 2y + 3z − 1 = 0 and the line 1: x= 1. Find the point of…

A:

Q: Question 5 Mrs. Parkes borrowed $6000 from her friends and family and was paying them back at a rate…

A: Given data:- Mrs. Parkes borrowed money from her friends &amp; family= $6000 paying back amount =…

Q: 1. ſ (x-1)dx x2+5x+6

A: The given integration is ∫(x-1)x2+5x+6 dx  We have to find the integration for the given integral

Q: What is the point-slope form of the equation that goes through the origin and has a slope of 1.5? y…

A: The point slope form of a line passing throught the point (x1,y1) and has slope m is  y-y1=m(x-x1).…

Q: Proor: Let † and g be one-to-one functions. a) Prove that (a) fog is one-to-one b) Prove that (b) (ƒ…

A: We will prove this using the concept of one to on

Q: On Integration by Parts [z√z+1dz fe* cost de [r³√³+1 da 1) 2) 3)

A:

Q: 4.1 4.2 Calculate the expenses to keep the Zoo open per day. Use a 30 day month. Tickets cost…

A: 4.1 To calculate the expenses to keep the Zoo open per day. To use a 30 day month.4.2 Tickets cost…

Q: A particle is moving with acceleration a(t) = 30t + 10. its position at time t = 0 is s(0) = 7 and…

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Q: (a)Show that F is a conservative vector field. f(x,y,z) = (b)Find a potential function for F.

A:

Q: For the following exercises, consider a pizzeria that sell pizzas for a revenue of R(x) = ax and…

A: This question can be solved using the concept of maxima and minima.

Q: The graph shows the rational function f (x) and the logarithmic function g(x). f(x)…

A:

Q: PRACTICE ANOTHER The graph shows the depth of water W in a reservoir over a one-year period as a…

A: Topic- Average rate of change of function over interval

Q: 2. Approximate v1.02 +0.02 using an function f(x)=√x + 1 + e*. appropriate local linear…

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Q: fa¹e² da dx: Applying the integration by parts technique, let Consider the integral Ա 4 X dv = ex x¹…

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Q: Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements…

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Q: 5.f 21 dv (v-1)(v+3)(v-4)

A: We can evaluate the given integral by using the partial fraction method.

Q: Which line has the greatest slope?

A:

Q: 5) Integrate 2x cos (x²-5) with respect to x.

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Q: Show that lim (x,y) →(0,0) 16x4 +9y¹2 4x² + 3y6 does not exist.

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Q: Consider the region bounded by x=4-1², the y-axis and the x-axis. N 1 1 2 3 4 The volume of the…

A: Given problem:-

Q: OS ng n Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of…

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Q: 17 0 dx √|x-1|

A: The objective of the question is evaluate the definite integral.

Q: dt 1²+8t+20

A: We can find the answer as below.

Q: If -2 5 [° f(x)dx = [__ * f(x)dx + [_^¸ ƒ(a)dx − [¯* f(x)dx, -8 what are the bounds of integration…

A:

Q: Suppose that a particle moves along a straight line with velocity v(t) = 13 - 5t, where 0 ≤ t ≤ 1…

A: Here the velocity function is v(t)=13-5t   , where 0≤t≤1 (in meter per second). We have to find the…

Q: : x-2y+3z-1 = 0 and the line 1 : x = Consider the plane 1. Find the point of intersection of and 1.…

A: Given: x-2y+3z-1=0x=1-y2=z+1

Q: e Find the volume generated by revolving the area enclosed by the loop of the curve y² = x (x-3)²…

A: Solution is given below:

Q: dy+y=x²y² X-

A:

Q: Define the force field F(x, y, z) = . a. Find the divergence and curl of F. b. Let C be the directed…

A:

Q: the graph below has the equation Ax + By = C, which statement MUST be true? A > 0 C = 0 B 0

A: From the given graph we can notice that the line passes through origin.

Q: Wants to know what will be the Maclaren series of g(x) = sin(x) is ?

A: Maclaurin series of function fx is a Taylor series of function fx at: a=0…

Q: 1 cot³ x dx =

A: To solve the given integral.