Given the vector u = <5,4>, find the magnitude and angle in which the vector points (measured counter clockwise from the positive x-axis, 0

Q: Let a be a number and let f, g, and h be functions defined on on Interval I about a. Suppose that…

A: Given: limx→afx=7, limx→ahx=3 To find:  limx→2facosπx, limx→afxfxgx+3hx, limx→33-xx-3

Q: Given, dr=b (cos@dr+rsin0d0) ; r(t) = 1, Find r(). 1 1+ b 1+b 2 1+b O b 1+b (1-b)

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Q: If f(-3) = -6, f'(-3) = -5, f(-1) = -18 and f'(-1) = -12 then: [ x . f"(x) dx

A: Given:- f-3=-6,f'-3=-5,f-1=-18,f'-1=-12

Q: Find the equation of the line tangent to the graph of f(x)=2x2−3x−3 at x=1.

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Q: X=1 #₂] x = 8 - 8x ²₁ x=0 Cotate x-axis 进了 X = 2 √SV kotate about x-axis Find Volume Y = ? X=0₁

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Q: The following integral requires a preliminary step such as a change of variables before using the…

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Q: The eccentricity of an ellipse is 0.5, and the length of the minor axis is equal to 20. Find the…

A: To find the distance between the foci of an ellipse.

Q: Prove that there is some positive number such that 07 - 20+ sin(02+1) = √5. Your proof must quote…

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Q: The equation of motion of a particle is s = t³ - 3t, where s is in meters and t is in seconds.…

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Q: Find the solution to the Bernoulli equation. xdy = ( + 7 - x) dx ○ y³ = 1+ Cx-³ Oy³ = 1+ Cx³ ○…

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Q: 13. r(t) = t sin ti + e' cos tj + sin t cos tk ht

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Q: For what value of k will the function f be continuous on (-∞, ∞)? f(x) = = +2 9 x + 3 k if x # -3 if…

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Q: Find c such that the function x ≤ c [x² - 8 10x 33 x>c f(x) = is continuous everywhere. C = с

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Q: Evaluate the integral. √3 [ arctan (1) dx 1

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Q: 3 f(x) = -2+x ... Select the correct choice below and, if necessary, fill in the answer box(es) to…

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Q: Evaluate the integral. (Use symbolic notation and fractions where needed. Use C for the arbitrary…

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Q: 8. Give a closed form for the sum You may assume that Σk=1 k = n(n+1) 2 1x2+2x3+ ... k(k + 1) and…

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Q: Using the Maclaurin series e = ∞ n=0 xn n! " ife find the general term of the Maclaurin series of…

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Q: (x, y) = (b) 1 1 (d) 1/2 Does not exist. (x, y) = Ty³ x² + y6 = Find limf(x,y) along the path x =…

A: We will find the required.

Q: Find the horizontal and vertical asymptotes. 2x² +9 f(x) = x²_ -9 Find the horizontal asymptote(s).…

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Q: -5 -3 7 n 4 3 2 hje -1 -2 -3 -4 2 3 -5+ In the above graph of y = f(x), find the slope of the secant…

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Q: en a rectangular box. Lengths are in cm 2 x X X

A: Given query is to find rate of change of volume.

Q: Find the area of the surface generated when the given curve is revolved about the given axis. y = =…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Convert the cartesian coordinates to polar coordinates with 0 0. (a) (-1, -7√³)=( 7 (b) (0, 7) = (…

A: a) The given cartesian co-ordinate is: -72, -732 Here x=-72, and y=-732  To cartesian co-ordinate to…

Q: A record company has determined that the cost of producing CDs is $0.06 per CD plus $597.60 per…

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Q: Evaluate the integral: [V4 Ox= √4x² 2x² -dx (A) Which trig substitution is correct for this…

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Q: let c1=(e^-4t,sin(t),3t^3) c2= (e^4t,cos(-5t),3t^3) d/dt[c1 dot c2]=? d/dt[c1 cross c2)=

A: Given :c1=(e-4t, sin(t), 3t3 )c2=(e4t, cos(-5t), 3t3)

Q: Find the volume of the tetrahedron with the given vertices. (1, 0, 0), (0, 1, 0), (0, 0, 2), (1, 1,…

A: The vertices of the tetrahedron are 1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 1, 2. We have to find the volume…

Q: Use logarithmic differentiation to find the derivative of y with respect to the given independent…

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Q: (a) f'(-3) (b) f'(-2) (c) f'(-1) (d) f'(0) (e) f'(1) (f) f'(2) (g) f'(3) y = f(x) 1 0 X

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Q: Solve the linear programming problem by the method of corners. Find the minimum and maximum of P =…

A: First we meed to draw the inequalities on the graph÷ Red line÷3x+5y≥20 Blue line÷-2x+y≤2 Green…

Q: Find parametric equations for the line through the point P(-3,4,-2) parallel to the vector 4i - 7j -…

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Q: Solve the following differential equation. Show your complete solution. 1. (1-x)y' = y².

A: (1-x)y'=y2(1-x)×dydx=y2dyy2=dx(1-x)∫yndy=yn+1n+1+c∫1xdx=lnx+c

Q: BOTH AXES FOR f(x) USE THE USUAL "1-2-3" SCALES y = f(x) Vertical intercept: Horizontal…

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Q: The graph of y = m(z) is given below. Answer each of the questions below the graph. 10+ 9 st…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Find any relative extrema of the function. List each extremum along with the x-value at which it…

A: Given  F(x)=-2+x3  Now ,For find the critical point we find the derivative of the function and equal…

Q: Find the distance from the point S(5, -6,6) to the line x = 10t, y = 6t, and z = 7t. The distance is…

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Q: 2a + bx Ex B f(x)=√√2a @f(x) = 3ax-5 x+b f(x) = 32²³ +26 ×-5c x-5c, a÷0

A: f'(x) = limh-&gt;0 f(x+h) - f(x)h This is the definition of derivative using limit.

Q: Evaluate f(x+3) when f(x)=x²-3x+4 (Be sure to simplify your answer)

A: Topic = Function

Q: The graph of f is given. State the numbers at which f is not differentiable. (Enter your answers as…

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Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by…

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Q: Find the velocity and acceleration vectors in terms of u, and up. r= a cos 30 and V= de dt v=4₁ + ¹₂…

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Q: Suppose that Find f'(z). f'(z)=0 f(x+h)-f(x) = 5hx² − 4hz - 6h²x+8h² - 1h³.

A: Finding the definition of derivative.

Q: Find d dx d dx 2 8x² 3 8x² 3 7 2 5x² 7 2 5x =

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Q: Estimate the area between the x-axis and the graph of f(x) = 9-2² over the interval [-2, 1] by using…

A: The given data is:   To find the area between x-axis and the graph of fx=9-x2 over the interval -2,1…

Q: Let f(x) Find the critical points of F and determine whether they are local minima or local maxima.…

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Q: Draw a graph to match the description given. G(x) is increasing over (-∞, -2) and (2,00) and…

A: Given query is to find the graph with Indicated properties.

Q: If z = xe², x = t³ and y = -3 + 5t then: dz dt

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Q: If the length of the smaler edge, x is increasing with time, x = t? (where t = time in seconds).…

A: given  x=tt is in seconds d dx(xn)=nxn-1

Q: 3. Assume that f(x) is continuous on [a, b] and x1, x2,...,n are arbitrary numbers taken from [a,…

A: The given data is: Assume that f(x) is continuous function on a,b and x1,x2,........xn arbitrary…