increasing decreasing f(x) = sin(x) + 1 T 2 + πn,∞0 0 < x < 2π (-∞0, 1/2 + 1) X X

Q: Work Problems ( your works 1) Let F(t)=(4t — t²)i+t² j+sin(5t — 10) k - - - You need to show all a)…

A: Given: Ft=4t-t2 i+t2 j+ sin5t-10 k

Q: Find (i) the net area and (ii) the area of the region above the x-axis bounded by y = 36-x². Graph…

A: Here we have to find the net area of the region above the x-axis bounded by y=36-x2 and the graph…

Q: Find ow/os and aw/ot using the appropriate Chain Rule. Function Values w = sin(7x + 8y) x = s+t,…

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Q: dy Find ck by implicit differentiation. √x+ y + √xy =4

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Q: Use the Ratio Test to determine whether the series is convergent or divergent. $ n = 1 Identify an…

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Q: x = 6 sin 0 is an appropriate trigonometric substitution for the integral Select one: True O False √…

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Q: Consider the infinite series > Evaluate the first four terms of the sequence of partial sums. k=1…

A: Given that infinite series       ∑k=1∞1k+3       We have to evaluate first four terms of the…

Q: random variables X and Y have the joint density f(x, y) = {1.5 (x² + y²),0 ≤ x,y ≤ 1, 0, elsewhere.…

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Q: Suppose that f'(x) = (x − 1)³x² x + 3 Determine the interval(s) on which y = f(x) is decreasing.

A: To find out the intervals on which the function is decreasing.

Q: dy 3. Find X by implicit differentiation. √x+y+√xy = 4

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Q: Consider the indefinite integral fe5z +6 dæ: a) This can be transformed into a basic integral by…

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Q: Integrate I -dz Select one: O A In 1-¹-2²+√1 − x² + C I OB. 21n1-¹³+√1 − x² + C | OC. In 1-²+√1 = z²…

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Q: Integrate √1 - r²dr Select one: OA. }(arcsinx+v1_2)+C OB. }(arcsinx+2v1_z)+C OC. (arcsinx +…

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Q: 2. Approximate In (0.93) using a Taylor polynomial with n = 3. Round your answer to seven decimal…

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Q: Əw əx aw ду Əw əz rentiate implicitly to find the first x² + y² + z²-7yw + 10w² = 9 11 || partial…

A: We can solve this as follows:

Q: SSR e-x² dxdy

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Q: Find the limit of the following sequence or determine that the sequence diverges. (-1)^) 4n+3

A: The given sequence,       -1n4n+3

Q: The result of the integral is equal to 4 √ = (x − 1)(x + 1) dx

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Q: 2. For Luce Landscaping, the total revenue and the total cost for yard maintenance of a homes are…

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Q: Solve the following first-order linear differential equations. Simplify your answers. dy dt ġ =…

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Q: Using Taylor Series, what is the value of yo(4) if y'=x+y² for y(0)=1?

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

A: Solution is given below:

Q: 4 (a² - y²)² 4. g(x) = (3x² + 4x - 5)5 3. 2 =

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Q: The gradient vector of the function f(x, y) = ln(xy) — x³ at the point (-1, 1) is (-1,-2). Select…

A: This question is based on gradient of function at a point.

Q: Find a normal vector to the level curve f(x, y) = c at P. X = x² + y² P(5, 5) f(x, y) = C = 100

A: To find the normal vector.

Q: Integral of sin^3 y cos^5 y dy

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Q: If 4x-2x² <f(x) <x²–2x+3 for all real numbers except for x=1, then Selected Answers: limf (x) = 2 x…

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Q: b) dx c) √₁² (3x² +4x−2)dx

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Q: For the function f(x) = sin² x, find the absolute maximum value M and the absolute minimum value m…

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Q: Answer the following True or False. 4ª + C In 4 faº f₁² da = True Faise

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Q: IV. Approximate the following up to 4 decimal places using Maclaurin’s series. 1. sin (110°) 2.…

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Q: At what point on the curve x = t³, y = 6t, z = t4 is the normal plane parallel to the plane 6x + 12y…

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Q: 1. Given f(x) = x² + 7x + 12 and g(x)=x²-9 Find (f+g)(x), (f-g)(x). (f g)(x), and ()(x). 2. Given…

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Q: 1. Find the domain of the vector function r(t) =< ln(t + 2), t 1 - 12 21 √12 - 4

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Q: E. (DERIVATIVES OF TRIGONOMETRIC FUNCTIONS) 1. If f(x) = secx + 3 csc r, then 2. If g(x) = x² sinx -…

A: To find the derivatives of the following functions.1 fx=sec x+3 csc x2 gx=x2 sin x-3x cos x+5 sin x

Q: The current population of a small town is 2848 people. It is believed that town's population is…

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Q: Compute the determinant of the matrix by cofactor expansion. 325 114 O-56 -8 O110 8

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Q: Calculate the volume of the solid bounded by the surfaces given by x2 + y2 = 1, z = 0 and z= x2 + y2

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Q: I. Anti differentiate the following. B. (ANTIDERIVATIVES OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS)…

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Q: +5t, y=s - 5t, z = st² d aw/ot by using the appropriate Chain Rule. d aw/at by converting w to a…

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Q: Write the first five terms of the geometric sequence. a 1 =  -5; r = -3

A: We can find the first five terms as below.

Q: Find the derivative of the following function. g(x)= 1+cos x / x + sin x

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Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A: Given that, the function is gx,y,z=xye8z and the points are P3,12,0 and Q0,0,0.…

Q: Compute the given integral. Enter your answer using exact values. fe-52 dx = +C

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Q: Which of the following is dž for t = 1 if dz dt 2t Z = In(x²y³), x = e¹ and y = e²¹ ? Select one: O…

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Q: Differentiate implicitly to find the first partial derivatives of z. x In(y) + y²z+ z² = 93 дz əx дz…

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Q: Let f(x, y) = domain of f is the set D = {(x, y)|x² + y² > 1}. Select one: 1 1 - x² - y² True O…

A: Given.

Q: 6. Find the values of at which the graph of f(x) = = 4x² - 3x + 2 has a tangent line parallel to the…

A: Follow the procedure given below.

Q: y(y² + 1)dx + x(y² − 1)dy = 0

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Q: Use the given information to find the exact value of the expression.  cos θ = 5/13 , θ lies in…

A: Given :cosθ=513