Use the following function to answer questions (a) and (b) below. 6-x, x<4 f(x) = + 3, x>4 (a) Find lim f(x) and lim f(x). Select the correct choice below and fill in any answer box(es) in your choim X-4* X4 (Simplify your answers.) OA. lim f(x) =, lim f(x) does not exist x--4* X-4 OB. lim f(x) = lim f(x) = X4* X4 OC. lim f(x) does not exist, lim f(x) = X-4* X4 O D. The limits do not exist. (b) Does lim f(x) exist? If so, what is it? If not, why not? X4 O A. No, lim f(x) does not exist because lim f(x)# lim f(x). X4 x→4* x→4 O B. No, lim f(x) does not exist because f(4) is undefined. X-4 O C. Yes, lim f(x) exists and equals X-4

Q: given the image use the area to calculate the following definite whole.

A:

Q: How would I find the limits?

A:

Q: 2. Use polar coordinates to find the limit. [ Please note that if (r,0)are polar coordinates of the ...

A: Consider the limit  limx,y→0,0e−x2+y2−1x2+y2    

Q: Optimization An open-top rectangular box is to have a square base and a surface area of 100 cm2. Wha...

A:

Q: If g(x)=3/x2, FIND g'(x) ALGEBRAICALLY

A: Answer is g'(x)=-6/x^3.

Q: The graph shown represents the graph of THE DERIVATIVE ƒ' (x) of an unknown continuous function f(z)...

A: Given, Graph of the f'(x) is shown as:

Q: Let f(x, y) = x 2 − y. Sketch the level curves for f = −2, 0, 1.

A: Given fx,y=x2-y

Q: Find the indefinite integral. Remember to include a "+ C" if appropriate.   ∫(10x 4−4x)dx=

A: Given,            ∫ 10x4 - 4x dx

Q: How can you tell whether an exponential model describes exponential growth or exponential decay?

A: An exponential model is of the form A=A0ekt where A0is the original amount or size of the entity at ...

Q: Does the limit exist?

A: Given limit, limx,y,z→0,0,0yzx2+4y2+9z2

Q: Two concentric circles are expanding, the outer radius at the rate of 5 ft/sec and the inner one at ...

A:

Q: Find the exact area of surface obtained by rotating the curve about the x-axis. y=sqrt5-x   3&lt; x ...

A: consider the equation

Q: Find the horizontal asymptote(s) and graph the function.

A:

Q: In a triangle, angle C and the two sides a and c are given as follows: C = c = V30, a = V10. (a) (6 ...

A:

Q: Find the second derivative  X3 + 4x2

A:

Q: Use a calculator to find the value of expression sin-1(-0.32) rounded to two decimal places.

A: we have given sin-1(-0.32)=sin-1(-0.32)  use the property that sin -x=-sin x    

Q: find (g o f)(x)

A:

Q: A particle moves along the x-axis with velocity v(t) = (6t 2 - t) mis.Find the particle's position s...

A: Given: vt=(6t2-t)ms, s2=4m we know that for position function we have to integrate given velocity fu...

Q: 2. Match the graph of each function in (a)-(d) with the graph of its derivative in I-IV. Give reason...

A: Now as it is asked just to match the graphs, * C matches with I * A matches with II

Q: 16-

A: The equation for the population growth is, Nt+1=6N11+N180 Consider the equation for Beverton-Holt mo...

Q: Determine the differential equation of the family of lines with its slope equal to the sum of its x ...

A: It is known that the equation of straight line is, y=mx+c Given that slope is equal to the sum of x ...

Q: 6. y = V2x – 3x . Find y'" -

A:

Q: Please show your work

A:

Q: Find the exact value of the expression tan(tan-1380), if possible. Do not use a calculator.

A: Use the formula  tantan-1x=x, x∈ℝ.

Q: on f(x, y) = 7x2 + 9y? - xy + x.

A: Let the function be, f(x,y)=7x2+9y2-xy+x. Differentiate the function partially with respect to x. ∂f...

Q: For the following exercises, find the change in volume dV or in surface area dA.   79. dA if the s...

A: surface area of cube is= 6 side2=6x2

Q: In Exercises 47-60, solve the initial value problem.

A: Givendydx=ex   y2=0

Q: You are walking to a bus stop at a right-angle corner. You move north at a rate of 2 m/sec and are 2...

A:

Q: find domain of (f o g)(x)

A:

Q: How do you find the derivative of f(x)=-7ln(x)+5x

A: Given: fx=-7lnx+5x

Q: find (f o g)(x)

A:

Q: The population of a city is 140,000.  It declines continuously by 4% per year.  Assuming this trend ...

A:

Q: For the following exercises, compute the values given within 0.01 by deciding on the appropriate f(x...

A:

Q: As water flows through a tube of radius R = 10 cm, the velocity v ofan individual water particle dep...

A: Given:  dv/dr = -0.06r, R = 10 cm To Find: v(r)  

Q: F(x) = xe", find f () %3D

A:

Q: In Exercises 61-67,firstfind f' and then find f.

A:

Q: How do I find the derivative.

A:

Q: 18h

A: Given: r→(t)=&lt;sin t, t, cos t&gt; We have to find V→(0): To get V→(t) : Differentiate r→(t) with ...

Q: 18b

A: Given,  r→t=sint, t, cost                   ...1

Q: It 3. Mow

A: The given statement is 3n≥2n+1 for any positive integer n≥1. To prove the above statement, we use th...

Q: 11 42x-1 + 14=

A: Consider the given equation: 11×42x-1+14=581 Subtract 14 from both the sides: 11×42x-1+14-14=581-141...

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.