Math

CalculusQ&A Libraryeither evaluate or explain why limit does not exist.lim f(x) as x --> 0 for (5 +2x+sinx) / (6cos x)I did substitution (5+2(0) + sin(0)) / 6cos(0) = (5+0+1) / (6 * 1)....BUT the book had (5+0+0) / (6 * 1).....struggling with why sin(0) = 1 and cos x = 0....as I thought when you find x the answer is y. so for sin(0) where x = 0 then why would this be 0? and same for cos(0) where x = 0, y would be 1 or -1??what is the logic behind how they are getting the numbersStart your trial now! First week only $4.99!*arrow_forward*

Question

either evaluate or explain why limit does not exist.

lim f(x) as x --> 0 for (5 +2x+sinx) / (6cos x)

I did substitution (5+2(0) + sin(0)) / 6cos(0) = (5+0+1) / (6 * 1)....BUT the book had (5+0+0) / (6 * 1).....

struggling with why sin(0) = 1 and cos x = 0....as I thought when you find x the answer is y. so for sin(0) where x = 0 then why would this be 0? and same for cos(0) where x = 0, y would be 1 or -1??

what is the logic behind how they are getting the numbers

Tagged in

Math

Calculus

Find answers to questions asked by students like you.

Q: I need help please.

A: Rewrite the given series and proceed further.

Q: How can I get the result? Which is the result?

A: The given function is,

Q: Find the area of the region that lies inside both curves. r = 9 + cos(θ), r = 9 − cos(θ)

A: To calculate the area of the given region (by integration) described by polar coordinates

Q: approximate the area under the graph of f(x) and above using the x-axis using the following methods ...

A: Given infromation:The given function is f(x)=2/x from x=1 from x=9.

Q: Find the area, in square units, bounded above by g(x)=6x−1 and below by f(x)=7x−15 over the interval...

A: It is given that region is

Q: How can I get the result? Which is the result

A: To find two positive numbers whose sum is 210 and whose product is a maximum.(a) Analytically comple...

Q: 18. CCT 11 The quantity (in pounds) of a gourmet ground coffee that is sold by a coffee company at a...

A: The quantity (in pounds) of a gourmet ground coffee sold at the price of p dollars per pound is give...

Q: Find all real values of x such that f(x)=0 F(x)= 18 - x^2/2 But then it asks me: Set the function eq...

A: The function is

Q: When converted to an iterated integral, the following double integral is easier to evaluate in one o...

A: Given information:The given integral function is shown below:

Q: s9-3x then y If y O 89-3x)4 25 O 819-3x)4 25 O 8(0-3x)4 O -24(9-3x)4 O 24(9-3x)4

A: The function is given by,

Q: Use any method to determine if the series converges or diverges. Give reasons for your answer.

A: Refer to the question.Here we have to find the convergence of the series,

Q: please explain how to find GINI Index if the lorenz function is Y=0.92x1.96 My answer book says the ...

A: The given Lorenz function is,

Q: Marginal Revenue. Suppose the total revenue function for a blender is R(x)= 36x-0.01x2 dollars where...

A: The total revenue function for a blender is R(x)= 36x-0.01x2 dollars where x is the number of units ...

Q: Find the relative maxima, relative minima, and points of inflection and sketch the graph for the fun...

A: We have to find the relative maxima, relative minima, and points of inflection and sketch the graph ...

Q: Please show as much steps as possible as I am doing my best to fully understand how to solve these t...

A: Given function is,

Q: a. find a possible function f and number a b. evaluate the limit by computing f`(a).

A: We first write the given function in the form of the definition of the derivative.

Q: a. find the critical points of f on the given interval b. Determine the absolute extreme values of f...

A: Given information:The given function is .

Q: Which of the following is the power series representation for f(x)? A. Σ ( -1): Ο Β. Σ 11k k 0 k 0 Ο...

A: In the given question we have to find the interval of convergence of power series representation for...

Q: Determine the location and value of the absolute extreme values of f on the given interval, if they ...

A: Calculation:The given function is f(x) = 2(5x)x defined on interval [0.05, 1].In order to find the l...

Q: During the first four months of employment, the monthly sales S (in thousands of dollars) for a new ...

A: Part (a)S= S(x)= 9 / x + 10 + x / 4, x ≥ 4The given function is defined only for x ≥ 4. We don't hav...

Q: Given f(x) = x^5 + x^3 - 4 , find the derivative of f inverse at the point (-2,1).

A: We are given a function as

Q: For the year data given in the chart find a power function that is used to model the Lorenz function...

A: A power function is of the form,y = axbWe can take log to the natural base “e” on the both the sides...

Q: Find the area, in square units, bounded above by f(x)=4x2 +9x−24 and below by g(x)=5x2+21x+3.

A: Given that, the area bounded above by f(x)=4x2+9x–24 and bounded below by g(x)=5x2+21x+3.Equate both...

Q: What's the domain of x-1 / (1 - e^(x - 3))

A: Since this function is a rational function, the denominator can't be equal to 0.

Q: A van is accelerating at a rate of 7 meters per second squared. The initial velocity of the van is 6...

A: Given: The van is accelerating at a rate of 7 meters per second squared. That is, a(t) = 7.The initi...

Q: A fence is to enclose a lot with area 100 square meters. The front of the fence (considered the east...

A: Let the length of the east-west side is = x meter and the length of the north-south side is = y mete...

Q: y = t(lnt)2 Find the derivative

A: According to the chain rule of derivative,Using the above rule, where u = t and v = ln t

Q: Consider the differential equation dy/dt = y−y2. Given that y(0)=0.5, solve the differential equatio...

A: To find the expression for y(t) and find the limit y(t) as t tends to infinity

Q: Define R as the region bounded by the graphs of f(x)=x2 +2x+2, x=−2, x=0, and the x-axis. Using the ...

A: Click to see the answer

Q: If y' 6x - 3 and y(2) 6 4, then y 3x2- 3x 3x2-3x-2 3x2-3x2 6x2-3x2

A: Given:

Q: I need help on how to contruct the definite integral needed to find the area of the geometric shape ...

A: Formula of area of triangle is = (1/2)*b*h, where b=base, h=height

Q: (3x2+5)8x-92 fy(1x4 + x2 logarithmic differentiation gives y (32+5)(8r-92 1x44+x2 16 2x 3x2+5 6-x9 6...

A: We have to find derivative using lograthmic differentiation .Question is given below:

Q: Find the domain: g(x) = ln(e^x -5)

A: The domain of ln z is z>0. We'll use the same concept here. So e^x-5>0.

Q: The rectangular coordinates of a point are given. Find the polar coordinates (r,0) of this point wit...

A: The given rectangular coordinates of a point is,

Q: How can I get the result? Which is the result?

A: The function is given as

Q: How do you set up the integral?

A: Given a triangle with function and the vertices,

Q: Hello, I need help explaining how pi(k)/2 came about, I know where pi/4 came from. Thank you for th...

A: Consider the provided trigonometry equation.

Q: 1. Estimate the volume of the solid that lies below the surface z = xy and above the following recta...

A: You have asked two unreleated questions in the same post. Further your first question has multiple s...

Q: A three times differentiable function fwith f'(x) 0 has a D-derivative at x given 2 f'"(x) 3(f"(x) D...

A: We’ll answer the first question since the exact one wasn't specified. Please submit a new question s...

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by th...

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

Q: How can I get the result? Which is the result?

A: The definite integral is given as

Q: Question: Find the area of the region bounded by y y0, x1, x-4

A: The area of region bounded by the curve y=(x^2+x-1)/((x)^1/2), x=1,x=4,y=0.

Q: How can I get the result? Which is the result?

A: The function is given by,

Q: Perform a first derivative test on the function f(x) 2x3x-12x +6, [-2,4]. a. Locate the critical poi...

A: (a)Locate the critical points of the given function f(x)=2x3+3x2–12x+6 on the interval [–2,4].

Q: How can I get the result? Which is the result?

A: we are given functions as

Q: Is y=ex +8x+5 a solution to the initial value problem shown below? y′−y=−8x+3 y(0)=6 Select the ...

A: The given differential equation is y’-y=-8x+3.The solution of the deferential equation is given as, ...

Q: Logarithmic Differentaition - see attachment

A: Given information:The given function is

Q: If given the differential equation y''-4y'+4y=et, is there a way to solve it for possible solutions?...

A: we are given a differential equation as

Q: How do I do this?

A: We are given a function and at a point

Q: The graphs of y=1.1x and y=x have two points of intersection, while the graphs of y=2^x and y=x have...

A: Here, we are given that for a real number 1< p < 2 , the graphs of y=px and y=x have exactly o...