5. What is the car's acceleration when they meet? Make sure to show work for this answer using Calculus, but you can use a calculator to find the your acceleration.

Q: Suppose you are standing in a field near a straight section of railroad tracks just as the…

A: As a first step, let's convert the given information in a diagram. Please see the white board.Let A…

Q: 7. If the tangent line to y = f(x) at (-1,3) passes through the point (2,1), find fl-1) and f'(-1).

A:

Q: Calculate two iterations of Newton’s Method to approximate a zero of the function using the given…

A: The function is given below fx=x2-5 and the the given initial guess x1=2

Q: 7)If a ball is Ehrown into Ehe air with a velociby of sIftis, it's height in feet after t seconds…

A: Please refer the attached image for complete solution.

Q: Find the length of the following curve. y = 2x + 4 on 3-2, 24 (Use calculus.)

A:

Q: 4. A. Use the tangent line to find a linear approximation to the function f (x) = Vx near x = 64.…

A:

Q: The slope of the tangent line to the graph of the function y = 8VI - 4 at (16, 28) is O 1.50 O -1.75…

A: Given function is, y=8x-4

Q: Find the equation of the tangent line to f(x)=−2x−4x^−1/2+3 at the point (4,−7).

A:

Q: Describe the Calculus approach to the tangent line problem

A: We have to describe the calculus approach to the tangent line problem.

Q: 10. y = Ce 2x

A: We have to find  orthogonal trajectory

Q: What happens if you apply Newton’s method to the function ƒ(x) = x?

A: we have to apply newton's method on the function ƒ(x) = x

Q: 4. Find the equation of the tangent line to g(x) 8 at x = 3 |x²–1

A: The function is given by gx = 8x2-13 To evaluate: The equation of the tangent line to the graph of…

Q: Use Newton's Method to approximate the zero(s) of the function f(x) = x' +4x +1

A: f(x) = x5 + 4x + 1 Basic formula for Newton's Method is: xn+1 = xn - fxnf'xn f'x = 5x4 + 41 + 0 =…

Q: What happens in Newton’s Method if your initial guess happens to be a zero of f ?

A:

Q: Explain why the two forms of Green’s Theorem are analogs of theFundamental Theorem of Calculus.

A:

Q: The slope of the tangent line to the graph of the function y = 8Vx – 3 at (9, 21) is %3D 1.33 -2.33…

A:

Q: Starting with x = 4 apply just two steps of Newtons Method to estimate 2, show work

A:

Q: Find the equation of the tangent line at (2, f(2)) when f(2) = 9 and f'(2) = 3. |3D

A: GIVEN FOR A FUNCTION f(x) ,f(2) = 9            &  f'(2)=3

Q: Find atleast three approximations of a solution of the equation f(x) = x – 2x3 0 by Newton Rampson…

A:

Q: 6. Find the equation of the tangent line to the parabola y 2.x2 – x + 3 at x = 2. %3D -

A: Equation of given parabola is, y = 2x2 - x + 3

Q: Use a linear approximation (or differentials) to estimate the given number. 99.8

A: To find √99.8

Q: 4. x*( 4x + 3y' ) = a

A:

Q: Two particles have positions at timet given by the equations x, =t -t and x, =6t2 -t°. Find the…

A: Given two position functions x1=t3-t and x2=6t2-t3 as a function of time t To find the velocities…

Q: The slope of the tangent line to the graph of the function y = 7 x – 3 at (9, 18) is. O -2.67 O 1.17…

A: We know that dy/dx gives slope of tangent at any point.

Q: Find the equations of tangent lines from S = 0 from the point A(0,0)

A:

Q: 4. x(4x? + 3у?) -а = a

A: Solution is given as below:

Q: Find all points on the curve 3x + 6y² = 36 where the tangent line also passes through the point (10,…

A:

Q: Explain any three drawbacks of Newton's method?

A:

Q: Calculate ∞0 1 e -3t √t - dt

A:

Q: If a stone is thrown up at 17 meters per second from a height of 170 meters above the surface of the…

A:

Q: Vehicle A is headed due west from a fixed point P at a rate of 45 miles/hour. Vehicle B is headed…

A:

Q: 9. y = x'(1- cx ) %3D

A:

Q: Determine the equation of the tangent to y 23.03x+y+13.03=0 23.03x-y-13.03=0 O-23.03x+y+13.03-0 None…

A: Solution ) y = 10x Differentiation with respect to x  dy/dx = (ln10) 10x [ Formula d/dx ax = ln a…

Q: .2 7. y= cx

A:

Q: 4. Find the smallest positive root of the equation a-r-10 = 0 using Newton Raphson method correct to…

A: Let fx=x4-x-10 ⇒f'x=4x3-1 Now f1=-10<0, f2=4>0 As f1f2<0 So,  by Intermediate value theorem…

Q: Discuss the two versions of the fundamental theorem of calculus

A: This the problem of Real Analysis, Theory of Reimann Integration.

Q: The slope of the tangent line to the graph of the function y = 8Vx - 2 at (4, 14) is . O-3.50 O2…

A: We will find the derivative of the function y and evaluate it at x = 4 to find the slope of the…

Q: 4. If f (2) = 3 and f'(2) = 5, find an equation of the tangent line at the point where x=2.

A: We have to find the equation of tangent.

Q: Find equations of the tangents to the curve x = 3t 2 + 1 y  =2t 3 + 1 that pass through the point…

A: The given equations of curve are Solving equations (1) and (2) by substituting the values of t from…

Q: 2x + 2 and the tangents to it at (1, 2 1 and 2 (4, 2) is

A:

Q: Find the tangent line to x^6 + y^6=2 at (1, 1).

A: Given : x6+y6 = 2

Q: What is the acceleration for s=3t3+20t2-10t+5?

A:

Q: 4. If s t-5t2 + 5t - 3, the velocity is equal to 2 if t =,

A:

Q: 4. Find the equation of the tangent line to the function y = In (x² – 2) when x=3.

A: Question is solved.

Q: 1. Find the equation of the tangent line to f(x)= 4x2 - 5x+2 at (-1,11).

A: We can find the equation of tangent to the curve as below.

Q: 22. If the tangent line to y = f(x) at (4, 3) passes through the point (0, 2), find f(4) and f'(4).…

A: #22 f(4) ? f'(4)?

Q: Please answer number 9 .determine the equation of the orthogonal trajectories of the following…

A:

Q: By Newton Method,

A: