Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (10, 12, -2) (60,24,156)

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Q: Let f(x) = 5 − 3x^2 + x^3 . (a) Find the intervals on which f is increasing or decreasing. (b) Find…

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Q: Evaluate F. dr along each path. (Hint: If F is conservative, the integration may be easier on an…

A: Fx,y,z=yzi+xzj+xyk

Q: Part I: Using the given data, follow the algorithm below to create a mathematical model which…

A: Given the data of population growth of a region. It is required to find the difference D in…

Q: Evaluate III. (x + y - 52) dV where E E = {(x, y, z) | Calculator Check Answer 5 ≤ y ≤0,0≤x≤y, 0…

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Q: (2) Let f(x) = sin(x²). Compute f(2023) (0).

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Q: This is for calc 1. Please find the area of the region. The two equations given were [2x+y^2=8] and…

A: The given equation of curves are 2x+y2=8 and x=y

Q: Suppose f(x) = √(x − 1) and g(x) = (2x − 3)/(x + 2) . (a) Find (f ◦ g)(14). (b) Find a simplified…

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Q: A tunnel cross section is formed by a rectangle 5m wide and 8m high with a rounded section at the…

A: Draw a schematic diagram of given figure.

Q: Evaluate r(u, v) ff. d5, where I = and S is the helicoid with vector equation 0≤u≤ 3, 0≤ ≤ 2m with…

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Q: Find the profit function for the given marginal profit and initial condition P(x) Marginal Profit dP…

A: dPdx=-20x+250 ,P4=$610

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Q: Suppose you drop a ball from a window 45 meters above the ground. The ball bounces to 65% of its…

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Q: Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal…

A: a=66,c=51,C=52° Figure

Q: Approximate the area under the graph of ƒ (z) = − 32² + 32 over the interval [1,9] using 4…

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Q: 3. Find the area inside one petal of r = sin(30)

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Q: The weekly revenue realized by a company is approximated by the revenue function = R(x, y) 350x +…

A: Given,   The weekly revenue realized by a company is approximated by the revenue function R(x, y) =…

Q: find derivative of f(x). f(x) = 3 x² - 4x3³+x+5 6x 12 x² +1 - Onone of these answers O 6x - 12 x² +6…

A: The given function fx=3x2-4x3+x+5. We have to find the derivative of the function.

Q: Calculate the limit L = lim (1-3x)6/* or show that the limit does not exist. If the limit is "+∞o"…

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Q: Evaluate the limit. limx→-1 f(x), f(x) = O-8 0-9 O 4 Does not exist. x²2 - 6x 10,x ≤ −1 X {₁ -2,x>-1

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Q: Suppose that f(x, y) = 4x +9y at which {(x, y) | -5 ≤ x ≤ 2, -5 ≤ y ≤ 2}. D Q Then the double…

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Q: The graph of the derivative f'(x) is given below. On what interval(s) is the function f(x) concave…

A: Given, the graph of f'(x).

Q: 6. Suppose Calculate (a) - 10 (b) -7 5 8 f(x) dx = 4 and 8 15 f(x) dx. 15 [ f(x) dx = -6. 5

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: · Verify: |_ Sin³x - It cosx in = COS X

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Q: 12) Evaluate the following: (a) Evaluate the definite integral: f¹(7 √x + 3x • √x) dx (Leave answer…

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Q: Determine the product of inertia with respect to the x and y axes for the area bound between the two…

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Q: Find the integral, S (1/x4) dx O /లు + c ○ 4x³ + c ○ // x5 + c O none of these answers

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Q: Solve the following differential equation: (x² − 2y²)dy + 2xy dx = 0

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Q: 8) (a) State the Mean Value Theorem. (b) Iff is a continuous and differentiable function on the…

A: Given data:-

Q: Suppose that f(x, y) = e/ at which {(x, y) | 0 <≤ y ≤ 1,0 ≤ z ≤y³}. D Then the double integral of…

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Q: dªy dx = 12x+2 :y(2) = 28, y(2) = 5

A: We need to solve the following differential equation: d2ydx2=12x+2 ; y'(2)=28, y(2)=5 This can be…

Q: Find the points at which the following function is discontinuous. 8x + 1 f(x) = 5x-8 6x²6 Select the…

A: The given function is f(x)=8x+1if x≤-35x-8if  -3&lt;x≤36x2-6if x&gt;3 Since polynomial functions are…

Q: 1. Sketch the following curves on separate number planes. (i) y=2x² (ii) x² + y² = 4 (iii) (x-1)² +…

A: since you have posted multiple questions i can do first question( with three sub parts) as per our…

Q: rmine the x-coordinates of any vertical asymptotes or removable discontinuities for the following…

A: fx=x-12x-32x-42x+53x-42x+14x-23

Q: 2. Consider f(x) = ax³ + x + 1, where a is a real-valued parameter. Find all possible values of a…

A: **As per our guidelines, we are supposed to answer only one question at a time. Since you have…

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to Then…

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Q: Give the derivatives of the following functions. There is no need to simplify your answers. 3 (a)…

A: The Power Rule: ddxxn=nxn-1 The Product Rule: f·g'=f'·g+f·g' The Quotient Rule: fg'=f'·g-g'·fg2 The…

Q: Find the value of dy/dx2 at the point defined by the given value of t. x=ty = St, t = 3 잉 0 굶 눕

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Q: Find the equation of the line tangent to the graph of f(x) = -x³-4x²-1 at x = -1. Provide your…

A: given  f(x)=-x3-4x2-1,  at x=-1

Q: Consider the following vector field. √x 4 + Z F(x, y, z) = i + √y 4 + X (a) Find the curl of the…

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Q: Find the area bounded by the parabolas y=6x-x2 and y=x2-2x I ONLY NEED THE GRAPH. LABEL IT PROPERLY…

A: GIVEN THAT              y=6x-x2              y=x2 -2x

Q: can you please annotate this and show all working out

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

Q: 15. Find all vertical asymptotes of the function x³ - 25x x4 -x3-20.x² g(x) = (a) x = -5, x = 0, and…

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Q: 5) Given h(x) = √√√8+x (a) Find the linearization of h at a = 0. (b) Use the linearization from…

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Q: f(x) = x² ex find derivative

A: Differentiate the given function  f(x)= x2ex

Q: The area of the surface generated by rotating the curve y = 2 = cos(4x), - where 0≤x≤ T/3, about the…

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Q: Use mathematical induction to prove that, for na 1, n²-n is divisible by 3. Note: If you would…

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Q: In polar coordinates, we have the unit vectors in the direction of and normal to as e, = cos 07 +…

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Q: Find an equation for the tangent line to the curve (x^2/9)+(y^2/36) = 1 at the point (−1, 4√2).

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Q: SIS dV, where E lines between the spheres x² + y² + z² = 4 and E x² + y² + z² 2 36 in the first…

A: To evaluate the given triple integral, we can use spherical coordinates because the integrand…