Suppose that a string is stretched and fixed at x = 0 and x = T. The string is plucked in the middle, which means that its shape is described by Sx, if0<æ < if 0 < x < f(x) At T, if - < < T 2 0 the string is released with 0. Find the t initial velocity g(x) displacement of the string as a function of x and t. Assume that for this string we have c = 0.002.

Q: (b) A poll commissioned by a politician estimates thatt days after he makes a statement denegrating…

A: Given: Percentage of constituency that supports a politician is: St=75t2-3t+25t2+3t+25 Derivative of…

Q: Q1) Find the Derivative to the function and find local minimum and local maximum points y = 3x? - 3

A: y=3x2-3 We need to find the derivative of the function and to find the local minimum and local…

Q: Suppose that f (0) = 2 and f'(x) 0. Show that f(4) 0.

A: f(0)=2   and f'(x)≤3  for all x&gt;0 ⋯(i)integrate (i) w.r.to x ,we getf(x)≤3x+kput…

Q: 6. Use the nth derivative test to show that -x has a maximum at x = 0.

A:

Q: Suppose that the p.d.f. of X is as given f(x) = 3(1-x)2 for 0<x<1 and 0 otherwise Find the pdf of…

A: If Y=g(X) is the transformation then the PDF of Y is given by; fY(y)=fX(g-1(y))ddyg-1(y)

Q: At which point is g(t) discontinuous?  g(t) = t^2+2, if t ≠ 1 -2, if t = 1

A: gt=t2+2,  if t≠1-2    ,  if t=1 The given function is continuous for all t≠1, because it is a…

Q: Function Point 53. y = x4 – 3x² + 2 (1, 0) 54. y = x³ + x (-1, – 2)

A: Solution Giveny=x4-3x2+2        (1,0)y=x3+x                  (-1,-2) We need to find the equation of…

Q: Find y as a function of t if 5184y" – 1584y + 121y = 0, - y(0) = 6, y'(0) = 3. y =

A: We have to find the general solution of the given problem.

Q: 4) The population of frogs has been declining in North Dakota. At one lake, researchers found there…

A:

Q: The graph of the DERIVATIVE of f(x) is below: 6 -6 -5 -4 -3 -2 -1 54 4 3 2 1 7 -2 -34 14 -5 -6 -7-…

A:

Q: Show that the function f(x) = K. when xw0 when xois discontinuous at x = 0.

A: Solution

Q: Write an expression that gives the area of the rectangle as a function of a. B. The area of the…

A:

Q: Find the first derivative: y = In V2r³ – 5 O y =: 22-5 O y = 4z 22-5 O y = 62 22-5 O y =; 2z-5 O y =…

A: Here we have to find the first derivative of         y = ln(2x3-5)1/3

Q: Compute the derivative of the following using product or quotient rules. oldetin nedi 1. g(x) =…

A:

Q: Let Compute f'(2). ƒ(x) = x³ + 3ª

A: This is a problem related to differentiation of the function. Please follow the procedure given…

Q: Find numbers a and b so that f'(1) exists for ax² + b 1 x² f(x) = if if x 1.

A:

Q: The amount, A, of anesthetics that a certain hospital uses each week is a function of the number, S,…

A: It is given that;  The amount, A, of anesthetics that a certain hospital uses each week is a…

Q: Suppose that f(x) is a function with f(180) = 35 and f'(180) = 10. Estimate f(180.5). f(180.5)

A:

Q: Suppose that f: R → R is a function with second derivative f"(x)=x•(x+ 1)³ · (x + 5)ª . Find…

A:

Q: We want to use the Richardson method to calculate the first order derivative antisymmetrically at…

A: We need atleast 2 points to calculate the Richardson second order derivative. The small parameter…

Q: Write all answers with numbers rounded to two decimal places. In Calculus the derivative of…

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.