What is the limit of (e^x-e^-x)/( sin (x)) as x approaches 0?

Q: find the limit as x approaches 1 from the right of  ln(x^9-1)-ln(x^7-1) using L'Hospitals' rule

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Q: Find the derivative of by the limit process

A: fx = 342-x

Q: 5. Use the limit definition of derivative to find f'(x) if f(x) = VT.

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Q: Use L' Hopital's Rule to find the limit as x approaches positive Inifinity of:  ln(x)-ln(1+x) Hint…

A: Given ln(x)-ln(1+x)

Q: limit

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

A: The given limit is,

Q: limit x approaches 0, (xcot2x)

A: Limit x-> 0 ( x/tanx ) =1Calculating the limit of the given expression using this result:

Q: What is the limit of (sinx)/x if x approaches to 0?

A: Given: A function limx→0sin xx and x approaches to 0. Since sin xx is an intermediate form of type…

Q: Find a limit if FedEx says if it does not exist right in DNE limit X to zero cosx tanx/2x

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Q: What is the limit as x approaches 0 of 2x/sin(2x)? Do so without using L'Hopital's Rule.

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Q: Use the limit definihon of the that gex)= derivative to show 9(x)= 3 3 has denvahre X+5

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Q: 2. Use L'Hopital's rule to find the limit; * - sin (*)= lim メ.Sin メーラ0

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Q: What are the formulas for differentiation and intergration? When to use them?

A: Query- What are the formulas for differentiation and intergration and describe When to use them?…

Q: find the limit. limit as x approaches 0  sin4x/sin6x

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Q: What is the connection of the concept of limits to slope to derivatives (delta method to simple…

A: The limits of the function at a point are calculated using the formula . The limits are used to…

Q: Estimate the limit numerically to two decimal places or state that the limit does not exist.

A: Given: limx→01-cos3xx2 we know that a3-b3=a-ba2+ab+b2

Q: What is the limit as x goes to infinity of (ln(x3 + 9) - ln(2x3 + 17x))?

A: Use quotient rule of logarithm to reduce the function as shown,

Q: find the derivative of the function the limit process. by flx) %3D

A: Given f(x)=1x2We know that derivative of f(x) with respect to x is defined…

Q: Please kindly use chain rule on the below to find the derivative and label all parts.  h(x)= cos…

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Q: Find limit sinax lim x→0 sinbx

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Q: Compute derivative of function using limit definiton

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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: compute limit as x goes to 0 of (sin(x)-x)/(x^3)

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

A:

Q: Find the limit.  limit as x approaches 0 sin3x/x

A: Apply the limits and find the in-determinant form.

Q: 3. y = at point (0, -) X-3

A: Topic = Derivative

Q: Express the limit as a definite integral on the given interval. lim Ax, [1, 4] (x;)2 + 3 dx Need…

A: Given query is to write the expression as integral.

Q: Find the derivative of y = arctan(x) by using implicit differentiation on x = tan(y).

A: Consider the provided function y=arctan(x).

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

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Q: Find the limit as x-->0 of sin(-3x)/sin(2x)

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Q: What is the second derivative of ecON (), , Cosh (A sinh?(x)e cosh (x) + cosh2(x)ecosh («) B sinh…

A: Let the given function is y=ecosh(x).

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: find the derivative by evaluating that limit , how do you simplify that limit to get the derivative?

A: We have to find the limit which is limit definition of derivative of f(t)=t^2-sqrt(t).Limit is given…

Q: cos 3z-cos x 8. limz0

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Q: What is the limit (as x approaches 0) of (sinx-tanx)/x^3?

A: lim sin x -tan xx3=lim sin x -sin xcos xx3=lim sin x cos x -sin xx3 cos x =lim (sin x x cos x)(cos x…

Q: lim(cos' x+sin 5x) tan 3x x→0

A: Given- limx→0cos3x+sin5x2tan3x To Find- The value of the above limit.

Q: How many times do you have to apply L'Hopital's rule to evaluate the limit x- sinx lim x+0 x²

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Q: Find the derivative by the limit process

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Q: Find limit   without using derivative

A: Given,

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

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

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Q: Differentiate the functions showing the general process in determining the derivatives. Using the…

A: We need to differentiate given function.

Q: How would I find the limit of the attached equation using L'hopitals Rule?

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Q: 12) Yex)=

A: The given function f(x)=6x

Q: What is the limit as x approaches 0 of 2x/sin(x)

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.