Problem 5: A particle moves along a line with a velocity given by v(t) = t² . - 2t where v is measured in meters per second. Find the displacement of the particle as well as the total distance traveled for 0 ≤t≤3.

Q: Suppose you drive 0.6 miles on a road so that the vertical distance changes from 0 to 150 feet. What…

A: Let the angle of elevation of the road be θ. Given that while driving 0.6 miles on a road, the…

Q: A ball thrown in the air has a velocity of v(t) = 98 32t ft/sec at time t seconds. Find the total…

A: given velocity is  v(t)=98-32t   given  t=1 to t=8 formula used is  v(t)=ds(t)dt∫xndx=xn+1n+1+c

Q: 4: A survey from Teenage Research Unlimited (Northbrook, Illinois) found that 30% of teenage…

A:

Q: f(x, y) = e 10x-z²+8y-y² Find and classify all critical points of the function. If there are more…

A:

Q: Suppose that the demand of a certain item is q = 50e-0.02p. Remember, elasticity is given by the…

A:

Q: Calculate the integral approximation Se for √₂ 741 dx. S6 =

A:

Q: What is d dx 7x 3x 2- sint dt? O-3√2-sin 3x +7√2-sin 7x O 10√2-sin x O-√2-sin 3x + √2-sin 7x O…

A: To find the derivative of given function

Q: Differentiate the following functions and simplify the answer: x 3/4 √√x² +1 (3x+2)(x-2)² a) f(x)=…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Given that y = 1.25%, write an equivalent equation in the form y = bx, with 0 < b < 1. y =

A:

Q: 1-4 Find the local and absolute extreme values of the function on the given interval.

A: To find the local and absolute extrema for the given function

Q: If the supply and demand functions for a commodity are given by 6p -q = 60 and (p + 2)q = 4830…

A: given  6p-q=60.......1           (p+2)q=4830........2from equation  1,   q=6p-60  put in euqation 2

Q: Imagine a spherical balloon filled with gas whose volume V is increasing at a constant rate of 3…

A:

Q: 1. Solve the following homogeneous differential equations and box your final answers. 4)v² dx + x(x…

A: We are required to find the solution of the homogeneous differential equationv2dx+x(v+x)dv=0

Q: area of the region enclosed between f(x) = x² + 2x + 11 and g(x) = 2x² + x − 1.

A:

Q: (2x + 3)y' = y + √2x + 3, when x = -1, y = 0.

A:

Q: Question Determine the second derivative of the parametrically defined curve represented by the…

A: given  x(t)=2t2-2t+4            y(t)=-8t3+8t2+4t+2dtndt=ntn-1d dt(ab)=bdadt-adbdtb2dydx=dydtdxdt

Q: 5. Find the values of a and b such that f(x) is differentiable everywhere sin x T sin x - cos x 2…

A:

Q: What is the general solution to the the differential equation3y"-y'- 2y = 10e*? A y=C₁e…

A: We need to solve D.E.

Q: dy Find L y = ln (2²+4) + + Icos HIN

A:

Q: use the Factor Theeorem to determine whether the first polynomial is a factor of the second…

A:

Q: 4. Given a function f(x) = 3x - 4 and the numbers xo = 2, L = 2, ε = 1. Then find a value 8 > 0 such…

A: Answer is given below

Q: Solve the equation algebraically, and then use a calculator to find the values on th [0,2π).

A: Given query is to find the solution of the expression.

Q: Use the Root Test to determine the convergence or divergence of the given series or state that the…

A: According to question,Given series,∑n=1∞n+33n+12n

Q: Find the value of the double integral 1 = [ S (6x - y) dxdy A when A is the region {(x, y): y ≤x≤…

A: this is question of integration  double integration is given  we have to find the value  further…

Q: Ab a \ B с [f(x)dx 0 C Area A = 1.573 Area B= 2.236 Calculate the definite integral by referring to…

A:

Q: The figure below shows the derivative f' of f. f ' (x) 4 10 + x मुंह 2 6 8 12 (a) Choose all…

A: We know Function increasing when f'x≥0Function decreasing when f'x≤0

Q: Evaluate the double integral I = √ √ (3x + 2) dA when D is the bounded region enclosed by y = x and…

A: To find:- I=∫∫D3x+2dA

Q: Suppose F'(x) = 5x² + 6 and F (0) = 1. Find the value of F (b) for b = 0, 0.1, 0.4, 0.8, and 2.0.…

A:

Q: 1. Find the definite integral using the Fundamental Theorem. Show in detail how the antiderivative…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: a) Evaluate 1 S (u + 2) (u − 3)du. -

A:

Q: 12. 1111111 Carefully explain, using diagrams and definitions as needed, what a scalar line integral…

A:

Q: Write an iterated integral of a continuous function f over the region R shown in the figure. Write…

A:

Q: Write the function in terms of the cofunction of a complementary angle. CSC CSC T 12 T 12 =…

A:

Q: 53. f(t) = 2 cos t + sin 2t, [0, π/2]

A: given 53) f( t ) = 2cost + sin2t interval - [ 0 , π2 ]

Q: find the general solution y cos x dx = sin^2 x dy

A:

Q: Find the area of the region between the curves y = ³ and y = 8x - 2x².

A:

Q: a) Find the derivative of f(x) = = 5 (t-1²)8 dt.

A:

Q: Suppose f'(x) = 8x³ + 12x + 2 and ƒ(1) = −4. Then f(−1) equals . (Enter a number for your answer.)

A:

Q: 1 4 3 N -2 -1- 0 -1+ y=5-x² 1 y = 4 R 2 y=(x-1)² 3 4

A: The given problem is solved below in detail.

Q: 5. x--1 According to the graph, does the lim g(x) exist? If so, what is the value of the limit? If…

A: A graph of the function is given, we have to find the limit of the function at x=-1.

Q: S ydy 2 A√/y²_9 Vy -9 4

A:

Q: У 2- -2- П 2л X

A: Graph of the function is given, we have to find its equation.

Q: Consider the following equation, if 0<x<1, periodic of period 2. f(x) = -2, if -1 ≤ x  ≤ 0, f(x) =…

A: The Graph is in step 2.

Q: a. Use the given Taylor polynomial p2 to approximate the given quantity. b. Compute the absolute…

A:

Q: asap

A: Please refer to the image below

Q: Determine the slope of the tangent line at t = 1 to the curve defined parametrically by the…

A:

Q: Find an equation of the hyperbola that has vertices (0,±6) and foci (0, ±7). Equation: 1

A:

Q: Consider the following curve. r = sin(20) Set up an integral that can be used to find the area of…

A:

Q: Determine whether the series converges or diverges: Input C for convergence and D for divergence:…

A: The answer is given below:

Q: What is the value of 06+In 8 06+In 2 S x² + 1 X dx?

A: