2.5 Continuity 85 40. lim sin 0 cot 20 0- 0 sin 3y cot 5y 42. lim y cot 4y y0 0 cot 40 44. lim sin? e cot 20 46. lim Cos2r x2 COS x a f(x) and lim,a f(x) at an interior point do you then know lima f(x)? Give reasons X- f(x) exists at an interior point of a domain find its value by calculating lim, f(x) C X- answer. Doag lnowinsth

Q: 1B) A red wine is brought up from the wine cellar, which is cool 10˚C, and left to breathe in a room...

A: Let T1 and T2 be the wine temperature and room temperature, respectively.

Q: It took a crew 3 h 36 min to row 6 km upstream and back again. If the rate of flow of the stream was...

A: Let the rowing speed in still water be x km/ hour.The rate of the flow of stream is 4 km/ hour.The r...

Q: Rewrite the expression by rationalizing its numerator. [sqrt(z-8)-sqrt(z)]/8

A: Multiply by conjugate in numerator and denominator.

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A: Here the initial amount of water in the pond is 600 liters and 30 liters are added for each minute.S...

Q: Calculate the average rate of change of the given function over the given interval. Specify the unit...

A: Consider the given table of the function

Q: Use the formula for instantaneous rate of​ change, approximating the limit by using smaller and smal...

A:

Q: 21 For the position function st)t+1. Complete the following table with the appropriate average veloc...

A:

Q: Find the volume V of the described solid S. A frustum of a right circular cone with height h, lower ...

A: The volume of the required frustum can be obtained as follows.Draw the frustum as shown below.

Q: = 3 and lim [3f(x) + Suppose f and g are continuous functions such that g(9)- 12. Find f(9) f(x)g(x)...

A: Given function is,

Q: lim x→∞ (sqrt(9x^2+x)-3x)

A: Multiply the numerator and denominator by the conjugate. Please see the white board.

Q: Can you help me step by step?

A: Given function:

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A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

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A: When he began the drive then x=0We have to find y when x=0y=375Answer: When he began his drive then ...

Q: On May 9, 2007, CBS Evening News had a 4.3 point rating. (Ratings measure the number of viewers.) Ne...

A: Considering p be the rating point and f(p) be the revenue earned in millions of dollars.

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A: a) Given that A(w)=539, we have to find w=?Answer: 19 weeks 

Q: Can you help me step by step?

A: The given function is,

Q: Can you help me step by step with this question please

A: Given information:A rock thorwn veritcally upward from  the surface of the moon at a velocity of 8 m...

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A: Given relation is:  A relation is said to be a function when for each input there is a single output...

Q: Can you help me step by step?

A: The given function is,

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A: Given line is: Equation of a line in slope-intercept form is y = mx + c, where m is the slope and c ...

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A: It is given that the half life of radioactive substance Cesium-137=30 years.And the amount A(t) of s...

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A: It is given that line passes through the point (-3,-9) and has a slope -2.

Q: See attached

A: To determine the exponential form of part (a) and logarithmic form of part (b).

Q: Graph the function and find the domain and range: y = x^2 + 5

A: We pick some values for x, for those we find ys by plugging the x values in the given equation.

Q: Can you help me step by step?

A:

Q: m of the tangent to the curve y 2 4x2 - 2x3 at the point where x a (a) Find the slope = m = (b) Find...

A: Given,

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A: The given information:

Q: How do I find a limit in terms of constant a? lim ((2/a+h)-(2/a)) / h h->0

A: Obtain the value of limit in terms of constant a as follows:

Q: can you help me step by step please

A: Given information:The equatio of the curve is

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A: The general formula for compound interest is A = P(1+(r/n))nt .Where A be the future amount and P be...

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A: We know that,                        Slope-intercept form is y = mx + bSince, the line passes throug...

Q: please look at c at the bottom example and sketch the derivative of the graph given. thank you

A: Since, the graph of function is given in different intervals.Below is the table of behavior of deriv...

Q: Find two vectors parallel to v of the given length. v PQ with P(1,7,1) and Q(0,2,5); length 84 The v...

A: firstly, we find vector v , that is vector PQ, which is equal to (position vector of Q)-(position ve...

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A: The point-slope equation is,

Q: Can you help me step by step?

A: Determine the derivative of function g(w) is 

Q: Express x2y2+ z2 = 2z in cylindrical and spherical coordinates.

A: Given,

Q: For the position function s(t) -16t103t, complete the following table with the appropriate average v...

A: To find the average velocities on the given time intervals for the position function

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A: The given equation is

Q: Can you help me step by step?

A: Find the derivative of the function

Q: A salesman drives from Ajax to Barrington, a distance of 166 mi, at a steady speed. He then increase...

A: Let us suppose that the salesman was driving between Ajax and Barrington with speed s mi/hr.Then his...

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A: The y-intercept of the line 12x-4y=-7 is computed

Q: Assume that 0 < 0 < 5. Find sin(20) and cos(20) if tan(0) (Give an exact answer. Use symbol notation...

A: Given,

Q: In 2010, there were about 246 million vehicles (cars and trucks) and about 308.7 million people in t...

A: Given,The rate of growth of vehicles =15.5 %And rate of growth of population =9.7 %Assume that after...

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A: 1 ton of sugar costs $150S ton of sugar costs $ 150 times S= $150S

Q: Calculate the average rate of change of the given function over the given interval. Specify the unit...

A: Given information:f(5)=12, f(1)=26, a=1 and b=5.

Q: Is the function f(x)= x+|x|-1 differentiable at x=0.

A: Consider the given function:

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A:

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A: (a) Rewrite the given equation as an exponential equation as,

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A: The given function, h is,

Q: Let P(x) 4x2 +6. Estimate the slope of the tangent line of this function at the point x = 5. (Give y...

A: Slope can be found using first derivative. We find P'(x).

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.