if x E Q 10. lim f (x) where f (x) = 10 if x e R\Q' х30

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

A:

Q: Evaluate lim f(x) where f(x) = x +2 cosx +1 e-4 for x20

A: Use the existence of limit definition

Q: why is the limit as x approaches 0 equal to 1/5 in the equation: ((sinx)/(5x))

A: The given limit is,

Q: For the function given by q (x)= x² + 2x+1, use the limit definition of the derivative to compute…

A: Definition of the Derivative:        The derivative of f(x)  with respect to x is the function f'(x)…

Q: Compute dy/dx using the limit definition of the first derivative for f(x) = 3x2

A: Given function is f(x)=3x2. we have to find the derivative using limit definition .

Q: If an object with mass m is dropped from rest, one model for its speed v after t seconds, taking air…

A: To find limit V , we will proceed as limit of function .V=mgc1-e-ctm

Q: express the limit as a derivative.

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

Q: Find the limit. y sin x limx.y)(0,1) O 1 8. O No Limit

A: Find the limit. lim (x.y)→(0,1) (y5 sin x)/x To select correct option  1 0 ∞ No Limit

Q: Find lim eR dt x 00 1/e 1 e

A: We will find first integration then after we apply limit

Q: (1 – e~*)* lim O 1/e -1 00 e

A: We have to find the limit of  limx→∞1-e-xex To find the limit we require a result that is If…

Q: Show that r sin (1/x) fails to have a derivative at r = 0 and even the one-sided limits (lim,-0+ (f…

A: We will prove the given statement.

Q: Suppose that f(x) is a differentiable function (with a continuous derivative), such that f(0)=…

A: To obtain the value of limx→03x-fx4x-fx, substitute 0 for x and 1 for f(0) in the expression, and…

Q: Evaluate the limit: sin(5x) cos(6x). lim x→0

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Q: sin xy lim 0.

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Q: Find the derivative of f (x) = Ln e*+1 using the limit process. %3D

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Q: Express the limit as a derivative.

A: Given, limθ→πcos θ-sin θ+1θ-π

Q: Find the derivative of the function by the limit process. h(s) = −2 (square root of x)

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Q: Find the limit of the transcendental function. lim x → T/2 4 sin x

A: Definition of limits helps to find the limit of the given function. The value is said to be the…

Q: Computing the derivative of ƒ(x) = x2 ex

A: Consider the given function fx=x2ex

Q: 1 Using the definition of the derivative as a limit, find f'(x) for f(x) x + 1 ||

A: Given that:

Q: If lim f"(x) = +00, then the trapezoid estimation Tn - f(x) dx O TRUE OFALSE can never be within…

A: Given,

Q: A tank contains 1720 L of pure water. Solution that contains 0.06 kg of sugar per liter enters the…

A:

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

A: See the attachment

Q: 1. To take the derivative of the following function. х т (1) y = m (2) y = x' log 2. To find out the…

A:

Q: If limit t y = f(x) write an expression for the differentia dy

A: Given: y=f(x)

Q: Express the limit as a definite integral on the giveninterval.

A:

Q: Find the derivative of f(x) = 1 at r = 0 using the definition of the derivative as a limit. Va +1 Be…

A:

Q: Use logarithmic differentiation to find for y = x4* %3D dx 2x Use LaHopital's rule to calculate the…

A:

Q: For f(x)=√7x+2, find f′(x) using the definition f′(x)=limh→0f(x+h)−f(x)/h. f′(x)= Using this, find…

A: Equation of the line passing through the points x1,y1 and having slope m is y-y1 =mx-x1.

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

A: we have to find the derivative

Q: If lim f"(x) = +0o, then the trapezoid estimation Tn - | f(x) dx %3D x0* can never be within 10¯³ of…

A: Given that limx→0+f''(x)=+∞ And Tn≈∫01f(x)dx Error for trapezoidal method contains double…

Q: cosx * sin? (3x) 2 2. lim x→0 x2

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Q: Express the limit as a definite integral on the given interval. lim 21 (x)2 + 7 Ax, [1, 8] dx

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Q: 8) Based on the graph of y = g(t) below, state the value of each limit if it exists. If it does not…

A: Observing from the given graph we have

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: Find the limits limx→0(ex + x)1/x

A: Consider the given limit as limx→0ex+xx

Q: Find the limit by interpreting the expression as an appropriate derivative. In (e10 + Дӕ) — 10 (а)…

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Q: Suppose that f(x) is a differentiable function (with a continuous derivative), such that f(0)=…

A:

Q: Find the limit.   Lim x→∞             (1+2x)5/2 ln x

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Q: verify that L’Hôpital’s Rule applies and evaluate the limit.

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Q: (a) By using the chain rule and the derivative (1, if x>0 4 (1xl) ={-1, if x<0 %3D find (lx-x) vxE…

A: Use the chain rule to differentiate the above given function and than use the given derivative of…

Q: x sinh x 1. lim x0 cos 3x -1

A: The solution of the problem is given in the next step.

Q: A tank contains 1980 L of pure water. Solution that contains 0.05 kg of sugar per liter enters the…

A:

Q: . Find the limit without using L'Hospital's Rule. sin 4t lim t-0 5t

A: We need to find the limit at t=0

Q: If lim f"(x) = +0, then the trapezoid estimation Tn - | f(x)dx x0* can never be within 10-³ of the…

A: Given that limx→0+f''(x)=+∞ And Tn≈∫01f(x)dx Error for trapezoidal method contains double…

Q: find the limit as x goes to infinity of ln(x+1/x+2)

A: Evaluate the limit

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

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Q: (2+h)* Use the definition of the derivative to evaluate lim h+0 h

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Q: Express the limit as a definite integral on the given interval. lim [9(x*)³ - 2x*JAx, [2, 9]

A: