We determined that l'Hospital's rule applies to the limit  lim x→5   x2 − 10x + 25 x2 − 5x

Q: Find the limit, if it exists. V(t + 25)(t – 1)² lim 11t - 11 t-1+

A:

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

A:

Q: 2. Find the derivative of a function at a certain number using the formula. f(x) – f(xo) f'(x) = lim…

A:

Q: 1. Find the equation of the tangent line of f(x) at the given point. f (x) = 6x – x2, (1,5)…

A:

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: Find the equation of the tangent line to the graph of y at (2, 금). Use the limit process in finding…

A:

Q: Let f(x) x + 1 Use the limit definition of the derivative to find the slope of the line tangent to…

A:

Q: Q1) A) Find the tangent equation for the function: f(x) = Vx² + 5 at =2 ? B) Find the limits by…

A:

Q: express the limit as a derivative.

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

Q: Let f(x) = Vör. f(x) – f(a) Using the definition of derivative at a point, f'(a) = lim enter the…

A:

Q: 5a) Using the formula man = lim+)=/G2 determine the derivative/ slope of tangent for h→0 the given…

A:

Q: a. Find the derivative of f(x) = x2 - 5x at x. That is, find f′(x). b. Find the slope of the tangent…

A: Given: fx=x2-5x To Find: a. f'x=?b. Slope of tangent line of the given function at x=-1 and x=3

Q: 4. Consider the function f(x) = Vx – I (a) Use the limit definition of derivative to find f'(x)

A:

Q: -10 For f(x) = 2x-3 show that f'(x) = e using the limit definition of the derivative. ind the…

A: (a) f(x)=52x-3 f'(x)=limt→xf(t)-f(x)t-x        =limt→x52t-3-52x-3t-x…

Q: Consider the function f(x) = V1 – 5x. a. Use the \underline{limit definition of derivative} to find…

A: We have to find the following given condition

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

A:

Q: Use the limit definition of the derivative to prove the following special case of the Quotient Rule:

A: We have to prove the following derivative by using limit definition: ddxfxx=x f'x-fxx2 We know for…

Q: All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the surface…

A: We have to solve above problem.

Q: The derivative of f(x) with respect to x is the function f'(x) and is defined as f'(x) = lim 0…

A: To find f(x+h) replace x by x+h in f(x).

Q: 4. Consider the function f(x) = Vx – 1 (a) Use the limit definition of derivative to find f'(x)

A: Ans:- Consider the function f(x)=x-1(a) we have to use the limit definition of derivative to find…

Q: (d) VT tanr - 2 V lim /4 VT x(4x – 7) Hint: divide both parts of the fraction by VT x and represent…

A:

Q: II. Compute the right-hand and the left-hand derivatives as limits to show that the following…

A: Given,

Q: Let f(x) = √x. Find the derivative of f(x) at x = 2 by using the definition of the derivative as a…

A:

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

A: See the attachment

Q: Q2/ Discuss the relationship between the derivative and (Lim) with drawing if it is dx required ?

A:

Q: 1. Suppose that the revenue (in dollars) from the sale of x units of a certain product is given by…

A: The revenue function is given by Rx = 70x-0.05x2 To evaluate: The expression of R'(x) using the…

Q: 3x g(x)=e* In(4x+1) (с)

A:

Q: Find (a) lim x--4- f(x), (b) lim f(x), and(c) lim f(x). X- -4+ x- -4 for x > -4 15) f(x) = ! x + 4…

A:

Q: Find the derivative of y = arccos 4x with respect to x.

A: Given that: y=arccos4x

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: Fill in the blank/s:

A: We have to fill in the blank.

Q: Find the derivative of the function by the limit process. f(x) = 3x- 1 - (x), J

A: fx=3x-1

Q: (b) y = tan x

A: Use limit method of derivative

Q: Find the derivative of the function f(x) = VI+4 using the limit process.

A: we have to find the derivative

Q: what the derivative fxy er hin ction Sas)=x'tan)

A:

Q: E. Set up the limit definition for finding the derivative of y = sin x.

A: Givne that  y=sinx  From the limit definition find the derivative of y=sinx

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: 5. Use the concept of limits to find derivative of f(z) = (2z + 1)3 at z = -i.

A: Given function is f(z)=2z+13 We have to find the derivative of the given function at z=-i.

Q: 8. For the function: 2 f(x) x +3' use the limit definition of the derivative to find f'(x).

A:

Q: 2. (a) Give the definition of the derivative f'(x) of the function f(x) in terms of a limit. (b) Use…

A:

Q: Find the derivative of the function. simply if possible y = arccos(e2x)

A: We have to find the derivative of the function: y=cos-1e2x We know the formula of derivatives,…

Q: 2.Given f(x)=5Vx-1, find f'(x)using the limit definition of the derivative.

A: Given f(x)=5x-1

Q: f(x) = 3-x/2x+

A: First we have to find derivative of function at x =-1 by using given forumla-

Q: II) By using the limit definition of derivative, prove the identity J dzf(2)8' (2) = - / da f…

A:

Q: Show that the following function is continuous at x = 1 for all values of p. (px + 1, if x > 1 f (x)…

A:

Q: Take the function (e 1>0 f(x) = %3D Compute its derivative at all values of x € R. Is f'(r) itself…

A: Given:   To determine: differentiation of f(x) and differentiability of f'(x)

Q: 3 Find the derivative with gicapeet to X If f(0 = 0-7 The derivatie with reapeet to X If -7X is…

A:

Q: Q1) A) Find the tangent equation for the function: f(x) = Vx² + 5 at =2 ? B) Find the limits by…

A:

Q: Determine the equation of the tangent line to •x³ +ln x the graph of f(x) at x = 1. [² = √/3 + 5t5dt

A:

Q: 2. Let x² sin () if x + 0 g(x) = if x = 0. Is g differentiable at 0? If so, find g'(0). Justify your…

A: Given: gx=x2 sin1x,       if x≠00,     if x=0 To Find: Is g differentiable at x=0? If so, to find…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: