Neglecting air resistance and the weight of the propellant, determine the work done in propelling a five-metric-ton satellite to a height of (a) 100 miles above Earth and (b) 300 miles above Earth.Use this information to write the work W of the propulsion system as a function of the height h of the satellite above Earth. Find the limit (if it exists) of W as h approaches infinity

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line.

A: Answer: f'(-2)=-1

Q: Show that the function has no limit as (x,y)→(0,0) f(x,y)=x4/(x4+y2)

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Q: Find the limit by evaluating the derivative of a suitable function at an appropriate point. Hint:…

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Q: Determine whether f is differentiable at x=0 by considering limh→0f(0+h)−f(0)h.   ​f(x)=18−x…

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Q: According to the theory of relativity, the mass m of a particle depends on its velocity v. Consider…

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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: Evaluate the limit or determine that it does not exist.

A: To evaluate the limit: limx,y→0xyx2+y2. Solution: We know that in polar coordinates, x=rcosθ and…

Q: Find the limits in Exercise

A: Given: limx→∞x2+x-x2-x To Find: The value of the given limit

Q: Find the limit and discuss the continuity of the function.

A: The function is given as,

Q: Evaluate the limit a x approaches positive infinity

A:

Q: Let a >0. Using just the e – 6 definition of the limit of a function, prove that lim V = Va. |r – a|…

A: The limit of function of f is given by,        Let I be an open interval containing c, and let f be…

Q: Estimate the limit numerically or state that the limit doesn't exist lim  h→0   5^h−1/h=

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Q: Determine the value of the limit if it exists. If it does not exist, explain why. ry? lim…

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Q: The derivative of a function of f at z is given by f(z+h)-f(z) f' (z) = lim h0 h provided the limit…

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Q: Question: What is the notation for "the limit as x approaches a from above of the function f (x) is…

A: Here we write the notation of the above statement.

Q: The figure shows the average daily population of a jail in the United States during the 1990s. j(t)…

A: To discuss continuity and differentiability (tangent) for the given graph

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (x, y) → (0, 0) x0 + y…

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Q: xy lim (x,y)->(0,0) x² + y²

A: We need to write down that the limit exist or not.

Q: Calculate the limit for the given function and interval. Verify your answer by using geometry.

A:

Q: In Exercises 29-46, equation of the tangent line. use the limit definition to compute f'(a) and find…

A: Given a function,  f(t)=2t3+4t and point a=4. To find the equation of the tangent line of f(x) at…

Q: Question: What is the notation for "the limit as x approaches a of the function ƒ (x) is infinity"?

A: The limit as x approaches a of the function fx is infinity

Q: Find the limit and discuss the continuity of the function.

A: Evaluate lim(x,y)→(2,4)x+yx2+1

Q: In Exercises 29-46, equation of the tangent line. use the limit definition to compute f'(a) and find…

A: The given function is fx=1x+3. Note that at =-2,  f-2=1 Compute f'-2 as follows.…

Q: Find the limit of  lim(x,y)→(0,0) (x^2 + y^2)/(sqrt(x^2 + y^2 + 1) − 1 rationalize the denominator

A: To find the limit value :

Q: Find the derivative using the limit definition. f (x) = x? + 5 f(x + h) – f(x) lim h h→0 lim (a +…

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Q: Determine the one-sided limits of the function f(x) in the figure at the points c = 1, 3. (If an…

A: Answer

Q: A. Evaluate the limit of a function using the concept of Special Limits. sin2t t3 sint 2. lim

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Q: Provide an example of a function of two variables with the desired properties (with justification),…

A: We will find out the required solution.

Q: What does it mean for a function ƒ(x, y) to have limit L as (x, y) → (x0 , y0)? What are the basic…

A: What does it mean for a function ƒ(x, y) to have limit L as(x, y) → (x0 , y0)? What are the basic…

Q: Lim secy-1 sec2y-1 a) as y → 0 b) as y → 1/2

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

Q: Determine whether the limit exists and if it exists find its limit value: x²y? lim (x,y)→(0,0) x² +…

A: Proceed as shown below...

Q: Find an equation of the tangent line at x = 2

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Q: Question: How else might you define "the limit as x approaches a of the function f (x) is L"? 3.

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Q: The L'Hospital's rule can be applied to find the limit of a function as long as you can express it…

A: L'Hospital's rule states that, the limit of the ratio of two functions is equal to the limit of the…

Q: Summarize limits of three special functions below. a. lim sint а. lim t-0 t 1-cost b. lim t-0 et-1…

A: (a) To find: The limit limt→0sin tt. Calculation: The limit limt→0sin tt is in the form of 00, Apply…

Q: ( Describe the end behavior of the function h(x) shown, using limits at infinity. 3 2.5 2 1.5 1 0.5…

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Q: Does the existence and value of the limit of a function ƒ(x) as x approaches c ever depend on what…

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Q: Find the limits. Are the functions continuous at thepoint being approached? lim y →1 sec (y sec2 y -…

A: We have given the function;

Q: 1. Cousider the funetion f(r) a- 1. (n) Find /'(r) using the limit definition of the derivative.

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

Q: Use a derivative (not L'Hospital's Rule) to evaluate (2 + h)4 – 16 lim h Enter the limit in the…

A:

Q: Question: If the limit as x approaches a of the function f(x) is infinity, does the limit as x…

A: To Determine: if the limit as x approaches a of the function f(x) is infinity,does the limit as x…

Q: sin²t t3 lim t-0 sint

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Q: Find a function f and a number a such that lim h→0 (2+ h)® – 64 = f'(a). %3D h

A: Given, limh→02+h6-64h=f'a

Q: „100

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Q: Write the limit as a definite integral and evaluate the definite integral. lim,0 E (15+8#)2 Enter…

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Q: valuate this limit forthe given value of x and function ƒ. ƒ(x) = x2, x = -2

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Q: Use the limit definition to find the slope of the tangent line to the graph of f at the given point.…

A: Use the limit definition to find the slope of the tangent line to the graph of f at the given point.…

Q: lim ilm f(x,y)=x²y²÷x²y² Calculate the two limits of the function

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Q: Calculate the limit for the given function and interval. Verify your answer by using geometry.

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Q: Evaluate the function f(h) at the given numbers (correct to six decimal places). F(h) = (2 + h}³ – 8…

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.