8. Consider an object moving along a line with velocity v(t) = 6t2 - 12t with t measured in seconds and velocity with units meters per second (m/s). Find the displacement of the object over the interval [0, 4].

Q: A smooth vector-valued function R(t) satisfies R(1) = (-3,7,9), R'(1) = (0,5,6) and R'(1) = (4, 1,…

A: Explanation of the answer is as follows

Q: 2) lim f(x) if f(x) = {x²43) X2² fx²-9, x2 x-2 F(x) X 2.75 2.5 2.1 2.01 2.001 X 1.5 1.75 1.9 1.99…

A:

Q: S x²-x+1 x² + 2x + 2 2 -dx

A: We need to evaluate integral.

Q: 9x3+3x²-12x Solve for the vertical asymptote/s of f(x) = 9x3+30x²+24x

A: To find vertical asymptote we will put the coefficient of y equal to zero.

Q: Q2/Find the value of the integral dx 1+x² by using simpson method (n = 6)? 3

A: Find out the value of the integral using the simpson 1/3 method.

Q: Evaluate the triple integral [ 2³ dV, where E is the solid tetrahedron with vertices (0,0,0),…

A:

Q: {CLO-2} Evaluate lim f(x) where (4x-1 if x3 O does not exist O 11 O 12 O 13

A:

Q: 3. Let R be the region below bounded by the parabola y = 4 – x² and the lines 3x - 2y + 3 = 0 and y…

A:

Q: 2. Write the given (total) area as an integral. a. The area above the x-axis and below y = 4 - x² b.…

A: Let's find  area between given curve and x axis.

Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f(x,y) =…

A: The quadratic and cubic approximation at (0,0) formulas are:…

Q: 4. Calculate the average value of each function over the given interval. Hint: use the identity sec²…

A: Average is evaluated.

Q: S 10dz 4z³-4z² + 5z

A:

Q: 0 2 -28 $² -2s e 8² -2s S O Option 3 -28 8 Option 1 -28 8 1 S 1 S 1 S + 82 O None of the choices e²s…

A: The answer is given below:

Q: Given R(t) = 4 costi + (1+ 3cost)j +5sintk. Find N(t) at t = = www. N(t) = ----k 10 Option 1 N(t) =…

A:

Q: -1 position (s, cm) 153 10- 5+ 0 2 3 4 time (t, seconds) 5

A: Slope of position(s) graph gives speed. i.e. Speed =dsdt

Q: Find the equation for the line tangent to the curve 2ey = x + y at the point (2, 0). Explain your…

A: Equation of tangent to curve is given.

Q: Q2/Find the value of the integral ²: by using simpson method (n = 6)? dx 1+x²

A: Let's solve given integration by using simpson 1/3 method.

Q: Consider the matrices shown below: Find the value of K such that 4 B-B2C-13 = 5 1 10 18 18 B-¹C – 15…

A: Given B=4-102 and C=142315We know that if A=abcd then A-1=1ad-bcd-b-caB-1=18+12104=192104

Q: valuate lim a. 12 b. C. d. +∞o t4-12 t-18 t3 0

A: The given problem is solved below in detail.

Q: ★ Each series converges. Show why, and compute the sum. k Σ[-88-(-3)*] k=2

A: p

Q: Given the polar coordinates (1,7π/8) determine (x,y). What is x=______. (round to 3 decimal)

A: In this question, we need to find the rectangular coordinates (x, y) from the given polar…

Q: √√5³-25² 2s + s ds

A:

Q: X1 (-1, 2) & (-3,0) Y₁ ; X₂ = m m 11 -C Y2 =

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

Q: Consider the following matrices: r 2 2 C# -H -N A = B = 30 1 € 4 1 0 -5_ Perform the following…

A:

Q: 'ind R(t) given R(1) = (1,0,−1). 'ind f'(1) if f(t) = (-2, -3t, t²). R' (t).

A:

Q: Syy-mat sama dy ³

A: Follow the procedure given below.

Q: The region bounded by the ellipse 16x^2 + 9y^2 = 144 is revolved about the x-axis. Find the volume…

A:

Q: 9-11. Solve the derivative using chain rule. y = x + 8x² + 16.

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Q: (a) Find the general solution of the differential equation d²y dx² +9y = x² + x + 1.

A:

Q: A Moving to another question will save this response. Question 11 {CLO-1} Find the values of a and b…

A:

Q: If u = x² tan equal to (a) (c) x - y x + y - 2 + V² 2 X X -, y x + y x - y x² + y² 2 X - y - y² tan…

A:

Q: Consider the following double integral - f By reversing the order of integration of I, we obtain:…

A: We have to reverse the order of given integral

Q: Numbers 13,14,15 please

A:

Q: Y y=√√√1-x² x Show that the volume under the surface z = 5x²y over the half of the unit above the…

A:

Q: aw Given w=xysin(z²), x=s-t, y=s², z t². Find www ax = ysin z² Option 1 aw əx Option 3 = -ysin z² Əw…

A: In partial derivative with respect to x, the terms of y and z are treated as constant.

Q: Stan ³0sec ³0 do let v = tan@

A: ∫ tan3θ sec4θ dθ

Q: A. Find the general equation of the conic with the given properties. A hyperbola with foci at (4-…

A:

Q: Given the function y = 8e-2x + 7 sec² 5x - 4 ln x³, find y'. Solution: 4(3)x² 3 12 X ------- 12 1…

A:

Q: Given the function y = 8e-²x² + 7 sec² 5x – 4 ln x³, find y'. Solution: y' = 4(3)x² x³3 +8(−4x)e-²x²…

A: We will find the y' of the given function in the following step.

Q: Find the general solution of nx dx = (x + 1)² ylnx

A:

Q: From the following table of values, find the approximate value of f'(1.5) 1.2 1.7 1.5 0.4055 f(x)…

A: Given

Q: If A = 3ai +4j-k and B = 4i+j-3k, find the value of a if A normal to B.

A:

Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y)=-3x²-3xy-8y²…

A: This is a problem related to maxima and minima of the function. Based on the general formula and…

Q: (CLO-2) The function f(x) = 2x³− 6x+4 decreases on 0 (-∞0,1) O (-∞, -1) U (1,∞) O (-1,1) 0 (-1,00)

A:

Q: Determine if the series converges or diverges Sum n=1 (n+1)/(n+3) State the test used, show that all…

A:

Q: Is f(x) = -3 A. Yes B. Does Not Exist continuous at x = 3? C. No D. Cannot be determined

A:

Q: Find the critical point and determine if the function is increasing or decreasing on the given…

A:

Q: Carbon extracted from an ancient skull combined only one-sixth as much as C14 as carbon extracted…

A: Let's find age of skull.

Q: Solve the DE by Homogeneous Equation 1. x y dx + (x² + y²) dy = 0

A:

Q: Find (au/ay) at the point (u,v)=(√6,-2), if x=u² + v² and y = uv. du = (Simplify your answer.) dy)…

A: ANSWER: 1