The position in feet of a race car along a straight track after t seconds is given by s(t) = 4t² - t + 5. Find its instantaneous velocity at t = 2 seconds. Provide your answer below: v(2) =

Q: 2 2(x + 1).In(x ² + 2x + 3) x²+2x+3 $² A) In(x²+2x+3) + c dx = ? B) In²(x²+2x+3) 2 +C

A: According to question,Given Integral,Let I =∫2x+1 lnx2 + 2x + 3x2 + 2x + 3 dx

Q: If g(x, y) = x² + y² - 6x, find the gradient vector Vg(1, 6). Vg(1, 6) =

A:

Q: Find the general solution of the following differential equation. 25y" - 25y' - 6y = 0 NOTE: Use c₁…

A:

Q: -1 Let f(x) = tan-¹ e²². Find f" (x).

A: The solution is given below

Q: Evaluate: [x(1-2²) da ¾ O ³(1-x²) + C 3 0-² (1-x²) O 3 + C O 2/(1-x²) + C 3 O ㅇ글 (1-22) : + C (1-x²)…

A: Here we have to find the integral.

Q: Use the derivative of a function definition to find f ′(a) at the given number a. f(x) = (5x+6)1/2…

A:

Q: Using the definition of the derivative, find f'(x). Then find f'(1), f'(2), and f'(3) when the…

A:

Q: The eigenvalues of the coefficient matrix A are given. Find a general solution of the indicated…

A:

Q: c. Given f(x) = 2x - 3, g(x) = -4x² + 9, h(x) = 4x² - 12x +9; find 1. f(x)* g(x) 2. h(x)/ f(x) 3.…

A: solve

Q: Q2A)Matrix 4 = [3] find Eigen values of 4².

A:

Q: Find a, b, c, and d such that the cubic function f(x) = ax3 + bx2 + cx + d satisfies the given…

A: Use derivative concept

Q: 14 Determine which statement is true Every simple graph is a complete graph. Every complete graph is…

A: below is your correct option

Q: If g(x, y) = x² + y² 6x, find the gradient vector Vg(1, 6). Vg(1, 6) = -4,12 Use the gradient vector…

A: Given that , gx,y=x2+y2-6x find the gradient vector ∇g1,6 and tangent line to the level curve…

Q: f 2³x dx = O 0 23x In 2 + C ○ 23x+1 + C 3x+1 23x In 8 0 23x ln 2 O + C + C

A: To evaluate: I=∫23xdx

Q: Fill in the blanks: 2² + 1 The equation describes an ellipse. The volume of the solid obtained by…

A: We need to find volume.

Q: Solve the equation 2x-1= 3x+1 algebraically.

A:

Q: Evaluate: xe² dx Ső 0e-2 0e² 1 - 0/(e-1) 22

A: Evaluate the integral

Q: Q5A) Find volume of body from above Z=√4-x² - y² and below Z Triple integration. 1 using

A:

Q: Write an equation for the function graphed below. The y intercept is at (0,-0.3) 5 4 3 2 1 + -6 -5…

A: We have to write an equation of given graph.

Q: Suppose that the total profit function for a company is given by P(x) = 4x³ - 210x² + 3600x - 200,…

A: We have to choose correct option for given questions.

Q: Give the equation for each graph. 5 4 3 2 1 -5 -4 -3 -2 -1 3 4 -1 5 -2 -D -4 -3 -2 3 -4 5 4 + 3 2 1…

A: 1.] The given graph is a line parallel to x - axis. The general equation of the line parallel to…

Q: calculate the lengths of all three sides using the distance formula of the non-right angle triangle…

A:

Q: B. Given that f(x) = {(-2,1), (1,4), (2,5), (3,6)} g(x) = 6 + 4x h(x) = -x² + 2 find

A: given

Q: 3 X and f'(-2) if f(x) = 6x. 8 (-2)=(Simplify your answer. Type

A: Given: f(x)=x38-6xTo find:f'(-2)

Q: Find the producers' surplus at a price level of p = $56 for the price-supply equation below. p=…

A:

Q: Evaluate x³ 2x² +7 dx S x² Ox² - 2x - 72 +0 0²-2x - 1 + C X O2+2 +c+C -2+7ln x² + C -

A:

Q: 14) A 300-foot cable weighting 4 pounds per is hanging from which 300 feet Level. Find ground the…

A:

Q: a dy Find given y = 4 In da

A: The given function,   y=4x lnx

Q: Differentiate implicitly to find the first partial derivatives of z. 2x2 + 11y2 + 3z2 = 36

A:

Q: Find the intervals on which f(x) is increasing and the intervals on which f(x) is decreasing. Then…

A:

Q: Evaluate the following integral. 48x² S dx (x-15)(x+5)²

A: Solution of given question is written in below steps.

Q: Solve for m ffm m(8xy + x?)dxdy =3, 0<y<x<1

A: we can solve as follows

Q: If f(x) = x² - 4, which of the equations below describes the average value of f(x) over the interval…

A: Let fx be a function, the average value of fx over an interval a,b can be calculated using the…

Q: Write the inequality in interval notation and graph the interval. -5<x<5 The interval is 0

A: Use interval notation

Q: 20 Which pair of graphs are complement of each other? V2 V2 VI V3 VA (a) (b) and (c) (a) and (c) (a)…

A: We have given, four graphs and we need to find out the complement of each other. Properties of…

Q: A balloon rises at a rate of 3 meters per second from a point on the ground 60 meters from an…

A:

Q: (7) ² Fi²+ Fi²+ ² Fi Fz Cos/20 49=F₁²+ F²-FiFe- tan 8= 48- = 4√3 4√3= F₂S in 190 Fit F₂ Golze $7…

A:

Q: (3x²-1) 5x3-5x+13 - dx equals In 15x³5x + 13| + c In 15x³ - 5x + c 5 O 1 In 15x³ - 5x + 13| + c 5 In…

A:

Q: Use the Inverse Function Theorem to find (h-¹)' (7) given that h(x)=√10x + 9. Note that h(4) = 7.…

A:

Q: The graph of f is shown. 8 (b) 0 8 16 24 32 Evaluate each integral by interpreting it in terms of…

A: According to the guidelines in case of multipart question,  we are only allowed to solve first three…

Q: Suppose f is a differentiable function of x and y, and g(r, s) = f(8r - s, s² - 7r). Use the table…

A:

Q: Use Euler's method with step size 0.1 to estimate y(0.4), where y(x) is the solution of the…

A: To solve the initial value problem.

Q: Determine the direction angles for the line with parametric equations x = 5 + 2t, y = 12 - 8t, and z…

A: Direction angle

Q: Find the general solution of the differential equation y" — 4y' + 104y = 0. NOTE: Use c₁ and ce as…

A:

Q: Hi, it is (-3)^n not (-2)^n

A: The given power series,∑n=0∞n2-n2nx+1n

Q: sint do соби Ө

A:

Q: Q1A)The vectors A = 3i+j+ 4k, B = 2i - 3j-k, find vector normal to A and In plane of A and, B. cos…

A: According to bartleby guidelines, we are supposed to do only one question. If you want more to be…

Q: Consider the following. de Use the substitution u = sin(0) to rewrite the given integral. SCC du The…

A:

Q: d dx (f³x²) = ○ 6x63x² (In b) ○ 6³x² (6 ln b) 6x6³x² ○ xb³x² (ln(6b))

A:

Q: A utility pole has a guy-wire attached to it 3 feet from the top of the pole. The wire is attached…

A: