Suppose that fis a continuous function and that1. f(x)dx=-1 and L(x)dx = 5, find the value of f(x)dx.

Q: The limit used to find the derivative is f(t) – f(x) dy dx lim definition %3D t- x

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Q: Find the derivative of the function by the limit process. 9. f(x) = %3D f'(x) =

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Q: 2. Use the definition = f'(x) = lim f(w)-f(x) to find the derivative of y = tan x. dx w-x

A: Let's take; w - x = h w = x + h As w approaches x; w-x = h →0   f'(x) = limh→0  [f(x+h) - f(x)]/(h)…

Q: Suppose that Xis a continuous unknown with -4< X< 4  having PDF denoted fsatisfying f ( x ) = c (…

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Q: express the limit as a derivative.

A: Given limit is: The limit definition of a derivative is given by:

Q: FIND THE DERIVATIVE BY THE LIMIT PROČESS OFF(x) = Vx+2.

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

Q: Use the limit definition to calculate the derivative at x = a of the linear function f(x) = 7.

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Q: Use the first derivatives test to find local exterma of f( x) =x3 -12x on R

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Q: Find the derivative of the function by the limit process. f(x) = 6/x

A: Given fx=6xddxfx=limh→0fx+h-fxh

Q: Suppose f(x) = df Find the derivative dx In(In(In(In(x)))). f' (x) :

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Q: Find f'(x) using the delta definition of the derivative (i.e., limit process) vhere f(x)= x² – 5x…

A: Given that        f(x) = x2 - 5x + 12 Here we have to find f'(x) by using the delta definition of…

Q: Discuss the relationship between the derivative dy/dx and (Lim) with drawing if it is required ?

A: See the attachment

Q: Find the derivative of f (x) = 2/x using the limit definition.

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Q: Compute the derivative of (arctan(x))^e^x

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Q: Suppose that a nonnegativefunction y = ƒ(x) has a continuous first derivative on [a, b] . LetC be…

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Q: Find the general anti-derivative of f(x) = + Vx on a continuous interval.

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Q: what is the differentiate of f(x)=ln x

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Q: 2. Find y' if y = 5x + 2 using the limit definition derivative.

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: / f'(x) sin x dx = 8, / f(x) cos x dx?

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Q: Find the derivative of f(x) = √x^2 + 1 at a = 2, using the limit definition (i.e. first principles)

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Q: What value for a will make sinx { ,X # 0 2x f(x) = %3D 3D ,X = 0 a continuous function?

A: For a function f(x) to be continuous at x = a,limx→a-f(x) = limx→a+f(x) = f(a)

Q: Find the derivative of the function by the limit process.

A: The given function is fx=-5x. Obtain the derivative as follows.

Q: Discuss the relationsh ip between the derivative dy/dx and(lim) with drawing if it is required

A: See the attachment

Q: fcx)= Y文 メ ー^

A: Local extrema

Q: Express the limit as a derivative.

A: Our Aim is to evaluate the limit of the expression given below:-limt→πsin (t) cos (t)t-π-(i)

Q: Give an example of a differentiable function ƒ whose first derivative is zero at some point c even…

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Q: Find the general anti-derivatives. Evaluate ∫ x/(x-1)(x+2) dx

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Q: Find the derivative of the function by the limit process. f(x) - f'(x) =

A: The given function is f(x)=4x2We have to find the derivative of f(x).

Q: n(x)=3x?4k+1 %3D

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Q: Find the derivative of the function by the limit process. f(x) = x2 − 5

A: Given function is By limit definition of the derivative

Q: Suppose f is differentiable with continuous derivative on [a, b]. Show that lim f(x) sin(nx) dr = 0.

A: To prove the given limit

Q: Is the functionf(x) = |x| cosx differentiable at the point x =0 ? (Use definition of the derivative)…

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Q: Shows that if a function f(x) is continuous in interval [a,b] then most likely the derivative of…

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Q: Ay Find the derivative of the following using lim Ax-0 Ar %3D dx ala

A: Part (a) - y = 4x2-5x       ...........(1)Given that,dydx = limx→0 ∆y∆x We can write it as - dydx =…

Q: Suppose for sume function f we heve its derivative, f'cx) = e*sin(x), on the %3D interval o< x< ar.…

A: fx is a function such that f'x=exsinx on the interval 0&lt;x&lt;2π We have to determine where the…

Q: 2. Use the definition = f'(x) = limw-x- S(w)-r(x). to find the derivative of w-x y = tan x.

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Q: Use Quotient Rule to find the derivative. x² + x - 2 3x +1: dy 2x+1 A. dx 3x + 1 dy B.…

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Q: Find an expression for the derivative  dy/dx If  y=tan(x2sinh(x)) A) dy/dx =sec (x2 cosh(x) + 2x…

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Q: f(x) = x*Inx

A: TO FIND 5th order derivative f(x) = x4 lnx FORMULA USED  BIPART PRODUCT RULE OF DIFFERENTIATION…

Q: dx 3-x

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Q: The first derivative of a continuous function y = f(x) is y' = x(x- 21). Find y" and then use the…

A: Given: i. The first derivative of a continuous function y=fx.ii. y'=xx-212 To Find: i. y''ii. Use…

Q: consider a continuous function y=f(x) whose first derivative is y'=x(x- 2).

A: We can find the interval as below.

Q: Use implicit differentiation to find dy/dx in x3 =2x - y/x + 3y

A: Here given as

Q: Use long derivative (dy/dx) y = cos x

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Q: show that the lim dose not exist x.y-00

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Q: Find the derivative by the limit process. F(x) = 13 -

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