Let g(x) = re) dt, where f is the function whose graph is shown. y f 2 12 2.

Q: 1. Explain why / f'(t) dt = f(b) – f (a). ||

A: Refer to image below.

Q: (1) Let g(x) :| f(t) dt. What is g'(x)? a

A:

Q: Assume that all variables are the function of t. If 5x2 - 4y3+3y=D7 and dy/dt 2 when x-11 and y=3.…

A: Take the derivative of the given equation with respect to t and substitute all the values than solve…

Q: Consider the function f(x, y) = y³ – 2y – x². Find the direc- tion of greatest increase at the point…

A:

Q: Find d2x/dt? as a function of x if d 6x sin x. dt? ||

A:

Q: If g(x) J.J S. 1 -dt , find g'(2).

A:

Q: x, 1 Let F(x) = J10 dt. Then (t + t7)15 F'(x) =

A: Let F(x)=∫axf(t)dt . If the function f is continuous, then applying the second fundamental theorem…

Q: dz dS 2 If S = z3 and -2 when z = 3, find dt dt

A: Derivative

Q: | f(t) dt = x*e* e + a

A: This question is based on integration.

Q: Use Euler's method to make the graph of the following functions on the given interval. a) dx/dt = t…

A: Introduction: The Euler's method is a basic and numerical method to approximate an initial value…

Q: secx 1 Given g(x) : z dt , find g'(x). t2

A: gx = ∫7sexcx1t2dt           = ∫7sexcx t-2 dt        = t-2+1-2+7secx      =t-17secx-1 = secx-1-7-1-1…

Q: Let F(x) = sin 3t dt, please find F'(0)

A:

Q: Use the Product Rule to compute the derivative: d. Find dt (e + 1)(t + 9)) at t = 13

A: Topic :- Derivative

Q: Assume x and y are functions of a third variable t. If xy = 20 and d = 10, find dy dt dt x = 4.…

A: u.v = uddx v + v

Q: 1losamlov ç5x3-1 Differentiate the function g(x) = [°*¯'sin t dt. -3

A: We have to differentiate the given function.

Q: Suppose f(x) = | sin(t?) dt. Find f'(x). x2

A:

Q: Use the Product Rule to compute the derivative: Find d/dt ((t^2+1)(t+9)) at t=5

A: To find  ddt[t2+1t+9]    at t = 5 Using Product Rule of Derivatives

Q: x and y are functions of a third variable t. If √√x + √= 5 and dt = 2, find when = dt 1

A:

Q: e If F(x) = | e dt, find F(1) and F'(x). ez

A:

Q: Find the derivative of the function. s = t In |t| ds dt 11

A: The objective is to find the derivative.

Q: Use the Quotient Rule to compute the following: d ( t2 +1 at t = -4 %3D dt \ t2 – 1 The derivative…

A:

Q: Find a value of x such that

A:

Q: 4x Let F (x) = S dt. Find F" (x). %3D 2+3

A: Given: Fx=∫04xdtt2+3 we know that by fundamental theorem of calculus if gx=∫pxqxfxdx then…

Q: 1. Let F(x)=√1+t² dt. Find F'(1).

A:

Q: If f(x)dx = 32, then f(t)dt : %3|

A: Here, Order of limit has been exchanged with each other.

Q: Let F (x) = (1 + t2)/5 dt - Then F'(x) =

A:

Q: Fill in the blank. = F(s - a) whereas L eat dt F(s - a) =

A:

Q: dy = 3 , find dt dx when x = 1 dt x and y are functions of a third variable t. If Væ + Vỹ = 4 and

A:

Q: Let f(x) /1+ In (t) dt. 2 f(e) = D

A: Differentiate wrt x

Q: Compute the derivative: d I/ In(t° + 1) dt dx

A:

Q: 2. If F(x)=[f(t)dt where f(t)= J -du , find F" (2). 27

A: if F(x)=∫1xf(t) dtWhere f(t)=∫1t21+u4udu

Q: If f(x) = | (t3 + 3t + 1) dt 0, then f" (x) = ||

A:

Q: 19 f(2) = | t² dt then f'(x) = If Find the derivative of g(x) = sin(t') dt. g'(x) =

A:

Q: 3t dt g(x) g'(x) = ||

A:

Q: E. Find , and in terms of dx dt' dt 1. x = t°- 1 2. x = 4t + 3 y = 3t – 2 y = 4 - t

A:

Q: a) If d'r = 3, when t = 0 we have dt? dx 0 and x=0, what is x as a function of dt t?

A:

Q: 1 Find F'(0) given that F(x) dt. In(t + 1) 2x

A:

Q: - (f* (t² + 1)¹⁰0 dt)" dt - Some ₁ tanx 1 + t2 d. y = e. y =

A: According to Leibniz integral rule : ddx∫a(x)b(x) f(x)dx=fbxddxbx-faxddxax

Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following.: y2 - 8x3 = -55; dx/dt…

A: y2-8x3=-55, dx/dt=-4x=2,y=3

Q: df Let f (x) = esinx and x(t) = t2 . Calculate a t = VT. dt %D

A: The given functions are fx=esin x  and  xt=t2. The given value of t is t=π.

Q: Find fr and fy- f (x, y) = 8e dt

A:

Q: g(x) f(x) - sin(2²) dt, find f(x). = J

A: To Find: f'(x)

Q: Given: y=fso(x-1) dt- d'y f(x)- dx show that 1 Add file

A:

Q: Assume that all variables are the functions of t. If 3y2-2x2+4y=2x and dy/dt =2 when x=5 and y=13.…

A:

Q: dx Suppose y = x4 – 2x + 1, and both x and y are functions of t. If dt when x = -1. dt = 2, find 12…

A: Given Data The equation is y=x4-2x+1. The derivative of x with respect to t is dxdt=2. x=-1.…

Q: Assume that all variables are the functions of t. If 3y2-2x2+4y=2x and dy/dt =4 when x-9 and y=12.…

A: Given,  3y2-2x2+4y = 2x   and dydt= 4  when x = 9  and y = 12  Then, we have to find the value dxdt…

Q: Let y=f(x), Given dy/dx=(3x^2 -1)/(2y) with initial condition f(1)=4. Find f(-2)

A: Given y=f(x), dydx=3x2-12y⇒y dy=12(3x2-1)dx⇒∫ y dy=12∫(3x2-1)dx+C⇒y22=123x33-x+C⇒y=x3-x+C Now, to…

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A:

Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.