Find the directional derivative of a funtion f(x,y,z)=x^2+e^xyz at point P(1,0,2) in the direction from P to Q (1,1,1). is this max rate of change ?
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a- Give an example equation of each of the common surfaces in this course (plane, sphere, cylinder, cone, paraboloid) and describe feature(s) that distinguish its graph from the others.
b- If you want to determine an equation of a line that passes through the point (0,0,1) and that is parallel to the xy-plane, how many such lines are possible and what do they all have in common? Give equations of at least two DIFFERENT such lines are part of your response.
In: Math
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1. For the function f(x)=x2−36 evaluate f(x+h).
f(x+h)=
2. Let f(x)=3x+4,g(x)=9x+12, and h(x)= 9x^2+ 24x+16. evaluate the following:
a. (fg)(3)=
b. (f/g) (2)=
c. (f/g) (0)=
d.(fh)(-1)=
3. Let f(x)=2x-1, g(x)=x-3, and h(x) =2x^2-7x+3. write a formula for each of the following functions and then simplify
a. (fh) (x)=
b. (h/f) (x)=
c. (h/g) (x)=
4.Let f(x)=5−x and g(x)=x^3+3 find:
a. (f∘g)(0)=
b.(g∘f)(0)=
c. (f∘g)(x)=
d. (g∘f)(x)=
5. Let f(x)=x^2+5x and g(x)=4x+5 find:
a. (f∘g)(x)=
b. (g∘f)(x)=
c. (f∘g)(0)=
d. (g∘f)(0)=
6. Let f(x)=x^2 and g(x)=x−5 find:
a. (f∘g)(x)=
b. (g∘f)(x)=
c. (f∘g)(5)=
d. (g∘f)(5)=
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Determine the centroid C(x,y,z) of the solid formed in the first octant bounded by z=16-y and x^2=z.
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Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
f(x, y) = x^3 + y^3 − 3x^2 − 9y^2 − 9x
local maximum value(s):
local minimum value(s):
saddle point(s) (x, y, f) =
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|
Convert 6∘ to radians, correct to 4 decimal places. 6∘= ____________ rad (4 dec. places). Convert 4.75 rad to degrees, correct to 4 decimal places. 4.75 rad = ____________ degrees (4 dec. places). |
Question b: (2 points) Determine the length of an arc of a circle with radius 6 metres that subtends a central angle of 300∘ to two decimal places. Arc length, s= ____________ m. c A circular wheel of radius 0.55 metres is spinning at a rate of 135 revolutions per minute. What are the angular speed (in rad/s) and the linear speed (in m/s) of a point on the circumference of the wheel to 2 decimal places? Angular speed, ω= ____________ rad/s (2 dec. places). Linear speed, v= ____________ m/s (2 dec. places) Determine the area of the corresponding sector of the circle with radius 6 and central angle 300∘ to two decimal places. Area of sector, A= ____________ m2. |
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1. Find all the values of x such that the given series would
converge.
∞∑n=1 (3x)^n/n^11
The series is convergent
from x = , left end included (enter Y
or N):
to x = , right end included (enter Y
or N):
2. Find all the values of x such that the given series would
converge.
∞∑n=1 5^n(x^n)(n+1) /(n+7)
The series is convergent
from x= , left end included (enter Y or N):
to x= , right end included (enter Y or N):
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Use Cavalieri’s principle to derive a formula for volume of a right circular cone.
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sketch a graph where the limit x-->2 exists but f(x) is discontinuous at x=2, what type of discontinuty is this?
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State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
4(x-1)^12(x+1)^7
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A rectangular box without a lid should be made with 12m2 of cardboard. What are the dimensions of the box that maximize the volume?
a.) 2m x 2m x 2m
b) 1.54m x 1.54m x 0.77m
c) 2m x 2m x 1m
d) 4m x 4m x 2m
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A rock is thrown upward from a bridge that is 59 feet above a road. The rock reaches its maximum height above the road 0.9 seconds after it is thrown and contacts the road 2.4 seconds after it was thrown.
Write a function f that determines the rock's height above the road (in feet) in terms of the number of seconds t since the rock was thrown.
f(t)=
Hint: the function f can be written in the form f(t)=c⋅(t−t1)(t−t2) for fixed numbers c, t1, and t2.
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An office supply company manufactures and sells X permanent markers per year at a price of P €/unit. The Price/Demand equation for the markers is: ? = 5 − 0.001?
1. Write the Revenues function (10%)
2. What level of production and what price should the
company charge for the markers to maximize revenues?
The total cost of manufacturing is: ?(?) = 3000 + 2?
Write the Company’s Profit function
What level of production and what price should the company charge for the markers to maximize profits?
Draw a graph representing the above-mentioned situation
Now the government decides to tax the Company in 1€ for each marker produced. Taking into account this additional cost:
Write the company’s new Cost function
Write the company’s new Profit function
What level of production and what price should the company charge for the markers to maximize profits (with these new conditions)?
(Please don't skip questions 5, 6, 7, 8, I need especially them)
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Problem 1
Part A: Write down an equation of the line L that is passing through the point A(5,4) and is perpendicular to the vector n=<-3,4>.
Part B: Find the unit vector u in the direction of n.
Part C: Find the distance d(Q,L) from the point Q(7, 13) to line L.
Part D: Find the coordinates of the point R on L that is closest to the point Q.
Part E: Now find R by solving the distance minimization problem using single-variable calculus. Which approach do you prefer?
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