(a) Approximate the definition of the derivative with small values of h. (b) Use a graphing calculator to zoom in on the function until it appears to be a straight line, and then find the slope of that line. 1/x f(x) = 8x ; a=4 (a) Select the correct choice and, if necessary, fill in the answer box to complete your choice. =(Round to four decimal places as needed.) OA. f'(a) = OB. f'(a) does not exist. ***

Q: 45° 8 Q The height of a right triangle with base angle 45° and hypotenuse 8 is

A: Answer: The solution is given below:

Q: Evaluate the limit: 1-cos 3h h lim h→ 12/2 -

A:

Q: Find the center and radius of the sphere. 2x² + 2y² +2₂² +x+y+z=25 Center = (1.1.1), radius= (Type…

A:

Q: Can someone please help me

A:

Q: Calculate the (modeled) probability P(E) using the given information, assuming that all outcomes are…

A: given  n(E)=6n(S)=24formula use is P(E)=n(E)n(S)

Q: t (seconds) 3 s (feet) 0 4.9 10.6 23.1 50.3 a) Find the average velocity (in ft/s) for each time…

A: According to bartleby guidelines we supposed to do the first one of multiple questions  kindly…

Q: Estimate f(g(2)): First graph y=f(x) Second graph y=g(x)

A:

Q: Given limx→6 f(x) = 8 and limx→6 9(x) = 5, evaluate If the limit does not exist enter DNE. Limit = 0…

A:

Q: Use the piecewise defined function shown below to answer the question. 18 (x+2)² g(x) = K - (x+4)² O…

A:

Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

A: Here is the integral .

Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the x²…

A:

Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

A: Here we have to find the limit.

Q: Use the following f(x) = (a) Find lim f(x). X-00 I 0=21212 O Does not exist. 8 -16 5 O 0 function to…

A:

Q: Find parametric equations for the line. (Use the parameter t.) the line through the points (-5, 2,…

A:

Q: Does the sequence {an} converge or diverge? Find the limit if the sequence is convergent. n an = 2n…

A: The answer is in step 2.

Q: A circular oil slick is expanding with radius, r in feet, at time t in hours given by r = 6t -…

A:

Q: Find the distance from the point to the plane. (0,4,-4), - 2y + 4z = 4 The distance is (Type an…

A: Given plane equation:- -2y+4z=4

Q: 63 X = 55° X 75° NOTE: The triangle is NOT drawn to scale. Find the following: Round your answer to…

A:

Q: Find the area of the surface generated by revolving the curve about they-axis. y=81-x²,05x59 A B…

A: Given :y=81-x20≤x≤9

Q: Use the graph below to fill in the missing values. -1 5 3 7 f(0) = f(x) f-¹(0) = 1 2 3 f(x)=0, x=…

A:

Q: ius, r, in centimeters, of a melting snowball is given by r = 60 - 2.5t, where t is the time in…

A: Given query is to find the volume formula in terms of time.

Q: Select the correct choice below and fill in any answer boxes i your choice. OA lim F(x)= (Type an…

A: Given query is to find the Indicated limit.

Q: The number of 3D movies released in a country in recent years is approximated by f(x) = In 2021 the…

A:

Q: The region R in the first quadrant of the xy-plane is bounded by the graph of y = x² + 1, the…

A:

Q: Find the vector, not with determinants, but by using properties of cross products. (j - k) x (k - i)

A: Given: ( j-k)×(k-i)

Q: ○a=3 O 10. Select the value of such that alog(x) is equivalent to log₂ (x). a=9 a = 1 3 Oa= √3

A:

Q: h (x, y) = 2xy + 3x² + 4x³y² +8 What is the value of Əh(x,y) dx when x = 3.8 and y = 1.5?

A: we need to find out the partial derivative.

Q: ector equation for this line is r(t) = (5, -4, 3) + t1, 4, - ½)

A:

Q: Given that f(-1) = -5 and f'(-1) = 4, find an equation for the tangent line to the graph of y = f(x)…

A:

Q: There are three possibilities when a line and a plane intersect in three-space. What are they, and…

A: Since you have posted multiple questions,  we are supposed to do only one question.  If you want…

Q: Use integration by parts to find the integral. ( √x xeax dx (a = 0)

A: Given integral ∫xeaxdx

Q: Find the sum of the series below. Σ n=1 48n (2n-1)² (2n + 1)² The sum of the series is.

A:

Q: Let f(z) = (1+15r cose + ar sine) +(3+ẞr sin0+6r cose), where z= r eie, be an entire function. Then…

A: Please see the below picture for detailed solution.

Q: The displacement (in feet) of a certain particle moving in a straight line is given by +3 2 y = =…

A:

Q: 1 9. Describe how the graph of y = log x + 2 relates to the graph of y=1 = log(x).

A: The given function y=log15x+2. We have to find how the graph of y=log15x+2 relates to the graph of…

Q: A graphing calculator is recommended. The displacement (in centimeters) of a particle s moving back…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Find the range of f(x) = 23 e*+3

A:

Q: Find an equation for the level surface of the function f(x,y,z) = . 2 +z through the given point…

A: we do only first part of multiple questions (1)  f(x,y,z)=x2+y2+z2

Q: 60° 14 The hypotenuse of a right triangle with base angle 60° and base 14 is

A: GivenIn the right triangleBase=14Base angle is 60°   We are required To find the hypotenuse

Q: Suppose f is a differentiable function of x and y, and the following applies. p(t) = f(g(t), h(t))…

A:

Q: Let g(x) = x² +Ax-7 x + 6 x ≥ 4 x < 4* Calculate lim g(x). x-4- Find the value of A that makes g…

A: The given function gx=x2+Ax-7,x≥4x+6,x&lt;4. We have to find the value of A, that makes g is…

Q: The population of deer in a forest can be modeled by 400x + 510 2x + 3 P(x) = where x is the number…

A:

Q: (b) Find the limits as x approaches 4 from the left and from the right. lim f(x) = X-47 lim f(x) =…

A:

Q: Given the function find the following. (a) the average rate of change of ƒ on [−3,3]: (b) the…

A: The given function fx=3x2-3x+5. We have to find the average rate of change of f on the given…

Q: How many steps does a limit proof have? What are they?

A: We have to write about the steps involved in limit proof.

Q: Suppose the position of an object moving in a straight line is given by s(t)=2t² +3t+5. Find the…

A: The position of a moving object at any time instant t is given by st = 2t2+3t+5 To determine: The…

Q: Given that f(x) = 9x - 8 and g(x) = 6 - x², calculate (a) f(g(0))= (b) g(f(0))=

A:

Q: 1. Evaluate the limits below. If they do not exist, explain why. Show your work (you can use any…

A:

Q: Suppose that 9x² +9x+7 < g(x) < 7x² − 8 x+7 for all x 0. Compute the exact value of lim g(x) x→0

A:

Q: Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region…

A: given  y=lnx, y=0, x=4 about the y axis formula for volume is V=∫abπ(R(x))2dx