Find the derivative of the function. 14 logg(t) t g' (t) = g(t) =

Q: For the function f(x,y,z) = 4x - 3y 5z + 1 find fx, fy, fz, and fyz. 9

A: f(x,y,z)= (4x-3y)/(5z+1)

Q: Consider the function f(x) function on this interval. = The smaller one is and the larger one is…

A: Given function:- fx=2x3-5x

Q: Select all the statements that are true. Assume that c is in the domain of f(x). ✔ limx→c (3x)² =…

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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list.) g(t) =…

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Q: A particle moves along the x-axis so that at time t≥ 0 its velocity is given by v(t) = 6t² − 24t +…

A: We have to determine the intervals when particle is moving right.

Q: Q3 Calculate the area of the shaded region in the given figure y Focus point Parabola curve P- 2p 8p…

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Q: 6 √√√m² +2+m6dm

A: Concept: Power rule of the integration ∫xndx=xn+1n+1+C Where C is constant

Q: Find the area of triangle with vertices Q C5, 1, 32, R (2,4,6), SC1,-1,9).

A:

Q: 1. Find a parameterization of the tangent line to r(t) = (- sin(2t), t², cos(2t)) at the point (0,2,…

A: Given :- rt=-sin2t,t2,cos2t

Q: Show that the surfaces are tangent to each other at the given point by showing that the surfaces…

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Q: Exercise 11 = (ƒ(x) + 5.x²)4 Let y = The Chain Rule and suppose that f(-1) = -4 and dy = 3 when…

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Q: A rectangular box has a width of 7 cm and a length of 1 cm. The volume of the box is decreasing at a…

A: Topic = Volume

Q: Find the partial derivatives of the function fz(x, y) fy(x, y) f(x,y) 8x - 7y 1x + 6y

A: To find partial derivatives,

Q: O 62 sin² (1) da = In(sin(x)) + 6 In(sin(x)) In(sin(x)) + In(sin(x)) (Apply integration by parts…

A: ∫u(x)v(x)dx=u∫v(x)dx-∫ddxu(x)∫v(x)dxdx ∫cotxdx=ln|sinx| ∫csc2xdx=-cotx

Q: Use the Ratio Test to determine all the values of t that will make the following series converge.…

A: Given series:- ∑k-0∞6·t2k-19k

Q: The radioactive isotope thorium 234 has a half-life of approximately 578 hours. (a) If a sample has…

A: Given is the question of radioactive decomposition.

Q: Use a linear approximation to approximate ln(0.98)ln⁡(0.98) as follows: Let f(x)=ln(x) and find the…

A: The given function is  f(x)=ln(x)

Q: - 1 x216

A: To evaluate the following integral.∫x2-1x2-16 dx

Q: du Evaluate at (x,y,z)=(4,3,0) for the function u(p,q,r) = e Pacos(r); p = = = ²1/₁, q=x² Iny, r=z.…

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Q: 1.23 Solve each of the following problems by direct integration. a. b. C. d. e. 4x = 3t 5x = 2e-4t…

A: As per the guidelines I am supposed to first question among multiple problems. So here I am doing…

Q: 9 Find the with a area of the parallelogram Verticles vertices; PC0,0,0), QC3₁=3₁-9), R (3₁-1₁-²5)…

A: I am attaching image so that you understand each and every step.

Q: (бх+34)

A: The given expression is 8x+3410. Formula used: Binomial expansion formula is :…

Q: Determine where the local maxima and minima occur on the graph given. -12 -10 -8 -6 -4 -2 12 10 8 6…

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Q: The cost function for folding bicycles is given by C(x) = 1450 + 900x + 0.1x² and the demand…

A: I am attaching image so that you understand each and every step.

Q: {2, y) = tans (2 I

A: Please see the below picture for detailed solution.

Q: Find the area of the region included between the parabola py2 = x and the line x + y = p.

A: The solution is given below

Q: Set up, but do not evaluate, an integral for the length of the curve. x = 7 sin(y), osys. 1. (C dy 2

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Q: Give your answer accurate to 3 decimal places. A man on a dock is pulling in a boat by means of a…

A: A man on a dock is pulling in a boat by means of a rope attached to the bow of the boat at a point…

Q: f(x,y,z) = 4x5+2xy-4z4 f(x.V.Z) =

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Q: If √ (2-4) (2 + 6) dr = Adr 2-4 Bdr +6' then A+B =

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Q: If $14,000 is invested and interest is compounded quarterly, determine the amount of the investment…

A: A=P1+rnnt ⇒A=Amount at time t⇒P=initial amount ⇒r=rate of interest ⇒t=time in yearsn=compounded…

Q: An initial investment of $30,000 is made in an account where interest is compounded continuously. If…

A: An initial investment of $30,000 is made in an account where interest is compounded continuously. If…

Q: Evaluate the following integral

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Q: A regression was run to determine if there is a relationship between hours of TV watched per day (x)…

A: Given data÷ y=ax+b a=-0.703 b=32.596 r2=0.491401 r=-0.701

Q: Given the function below 3 25 g(x) = X x+1 Which of the following leads to the solution of the…

A: Topic = Function

Q: Find the inverse transform of the given function of s. 5 F(x)=-=-/ (A) There is no correct answer…

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Q: Let f(x) = x( 1 — [1]) and g(x) be any function. Prove by epsilon-delta definition that lim g(f(x))…

A: Limit

Q: lim (1 + sin 3x) x→0+ CSC 2x

A: We need to evaluate:

Q: 2. Given r(t) = (2, e³t-3, 6t+2) with r(1) = (2, 1, 7) and r'(1) = (2,0, 5), find r(t).

A: The objective is to find r(t).

Q: 5 Invert the matrix A 8/1+10/2+713 = 0 511 + 912+4/3 = -9 = 1. 91+11/2+8/3 8 10 7 594 9 11 8 and…

A: Please see the below picture for detailed solution.

Q: Use linear approximation, i.e. the tangent line, to approximate 1.954 as follows: Let f(x)=x4 . The…

A: need to find out by linear approximation the value of 1.95⁴

Q: dy Use implicit differentiation to evaluate at the point (-2, 1). dx (Submit an exact answer.)…

A: Topic = Derivative

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y₁…

A:

Q: Determine where the graph of f(x) = 2x³ + 27x² − 45x-60 is concave down. f(x) is concave down where…

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Q: Let f be continuous and twice differentiable function such that f is increasing and concave down and…

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Q: Find the equation of the tangent plane to the surface z = cos(5x) cos(6y) at the point (2π/2, π/2,…

A: The equation of the tangent plane to the surface ?=?(?,?) at the point (?,?,?(?,?)) is…

Q: The area under the curve y Square Units 5x bounded by the lines x = 9 and x = 26 above the x axis is

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Q: -9 -8 (-inf,) -7 -6 -5 -4 -3 a. Select an x-value in the first interval, (-∞, - 2/2 ): -2 -1…

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Q: Find the critical numbers of the function. h(t) = 3/4 - 2¹/4

A: Topic = Derivative

Q: Continuing with the same graph of f(x), which value is the greatest: f(5), f'(5), or f(6) -f(5) ?…

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