Consider the graph of f(x) given below. y = f(x) (a) Analyzing the graph, if g(x) = f(x), then g is decreasing for x € (b) Analyzing the graph, if h'(x) = f(x), then h is decreasing for x € Note: Input U, infinity, and -infinity for union, ∞, and -∞o, respectively.

Q: Consider the following. u = 5i + 2j v = -6i+j+ 2k Find u x v. Determine if u x v is orthogonal to…

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Q: (c) (d) S. 25 ∞ 2x³ dx 1 -2x +4 dx

A: c) d)

Q: Solve the equation and inequalities. Write the solution sets in interval notation if possible. (a)…

A: To solve the following equation and inequalities.(a) (b) (c) (d) (e)

Q: 0 18. (sin x- — π 4 π 4 1)dx + f (cos x + 1)dx 0

A: we have given integration

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Q: Use the Law of Cosines to solve the triangle. Round your answers to two decimal places. a = B = BO…

A: We have to find remaining sides and angles for the given triangle

Q: Solve the given differential equation by undetermined coefficients. y" + 4y = 4 sin(2x) y(x) =

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Q: lim arctan((z 8118 00 OT/2 =

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Q: Find the curvature of the curve (t) = (3-2 cost, -1, 4+2 sint) at the point t = -π. 3

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Q: The deflection D of a beam of length L is D = 7x4-9Lx³ + 2L²x², where x is the distance from one end…

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Q: Verify the following identity: 1 sin² x 1+ cos x = cos x

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Q: 6. Show that for any cubic function of the form y = ax³ + bx² + cx+d there is a single point of…

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Q: b.F(K, L) = (Kª + Lª)¹/ª → KFk+ LFL 3t c.g(t, w) = 3 + wt². W 8² g Iw It = = d.g(t₁, t2, t3) = (t +…

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Q: The wave equation of physics is the partial differential equation o'y d²y at² əx² Where c is a…

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Q: 21. lim 1→+∞ 6-t³ 71³ +3

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Q: C. (I +3A)−¹ = 2 1 0 -1

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Q: Find and simplify the functions (f+g)(x) and (f-g)(x). f(x)=x^(2)-7 and g(x)=x^(2)-10

A: We know that the formula(f+g)(x)=f(x)+g(x)

Q: Find u x v, v x u, and v x v. u = 4i + 7k v = 6i + 9j - 5k. (a) ux v (b) (c) V x u V X V

A: We have given two vectors u and v and we want to find the cross product of the given vectors in…

Q: Find the derivative of the following function. y = 4.5x

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Q: Verify the following identity: sin(a+B) + sin(a - B) = 2sinacosß Use the paperclip button be

A: We use the sum to product formulas to prove the given identity.

Q: Let f be the function given by f(x) = 300x - x³. On which of the following intervals is the function…

A: f(x) = 300x - x3

Q: Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle. a = 10, b…

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Q: Consider the following vector field. F(x, y, z) = 3xye²i+yzexk (a) Find the curl of the vector…

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Q: (b) | x-3 x(x² + 2) dx

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Q: 9. Find a power series representation for f(x) = = 8 4+x

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Q: years is given by The amount of carbon-14 present in animal bones after t P(t)=Poe-0.00012097t. A…

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Q: Two poles, one 6 meter: tall and one 15 meters tall, are 20 meters apart. A length of wire is…

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Q: Let s(t) = 8t³ + 12t²-144t be the equation of motion for a particle. Find a function for the…

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Q: 2 37. f(sec²x 2 tan"x) (tan x sec x sec x) dx

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Q: SC y Jo Jo (xy + 1) dy

A: The given integral is:

Q: Consider F and C below. F(x, y, z) = yzexzi + exzj + xyezk, C: r(t) = (t² + 5)i + (t² − 1)j + (t² -…

A: And  ,

Q: d da cos(3) = O-3 sin (3²) O 32.cos(3²) -3.sin(3²).In 3. O sin (3²) O3 cos(32).In 3

A: Given

Q: 23. If x² - y² = 9, find dy dx 24. Find f'(x) if f(x) = X

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Q: Using first principles, determine the equation of the tangent line to the curve y= 1/3x^2 when x=-1

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Q: How many solutions does the following equation have on the interval [0, 2]? 4cos28=8cos²20 4 9 0 8

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Q: Evaluate cos(+3) using fundamental trigonometric identities. 4 o vž 8°F Partly sunny F1 O -√2 ! 1 Q…

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Q: Let C be the curve y = 7x³ for 0 < x≤ 2.3. 81 72 63- 54 45- 36 27- 18 9 0.5 1 15 2 Q Find the…

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Q: Determine which set of vectors is not orthogonal. v = (-10,0), w = (0,5) v = (0,1), w = (0,1) O O v…

A: If two vectors are orthogonal then the dot product of the vectors is 0.

Q: 2x x 2 sin Evaluate the spherical coordinate integral p² sin dp do d0. 000 The value is (Type an…

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Q: Determine whether each of these functions is a bijection from R to R. If it is, rite the inverse…

A: We have to check whether the given functions are bijective or not

Q: Find the eigenvalues of the symmetric matrix. (Enter your answers as a comma-separated list. Enter…

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Q: Find the general form of f if f'(x)= -7f(x).

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Q: n = 0 (-1)^n! (x-9)" 5"

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Q: Determine a region whose area is equal to the given limit. Do not evaluate the limit. lim Σ Σ(1+2) i…

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Q: Evaluate the following integral. x/2 SSISK ² 24p cos ³¶p dep d0 dp 3

A: we have given integration

Q: 37. Find: d dx (125x)

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Q: w = 9z²e²

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Q: Find the derivative of: Vz HINT: recall that I = 2². Write your answer using negative, fractional…

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Q: F Ifv = i +2j and w = 3i + 6j, then the projection of v onto w is: O i+2j O-31-6j O 11-2j 3i+ 6j Q…

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Q: Without using a calculator, what is the value of the following fun cos(130°) cos(10°) + sin(130°)…

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