Practice 4: a) Find at least the first eight derivatives of pattern you observe. sin.x and observe the pattern that occurs. Write out the b) From the pattern you observe in part a). find the derivative: d23 dx sinx

Q: Solve the inequality. Write the solution set in interval (+5)(y-1)(y-6) ≥0

A: (y+5)(y−1)(y−6)≥0

Q: a. b. C. Find the derivative of the function. y = sin(tan(7x)) Find the derivative of the function.…

A: According to Bartleby answering guidelines, we can answer only first three subparts. Kindly post…

Q: Find a Cartesian equation for the curve. r = 9 cos(0)

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Q: . D11: I can use derivatives to solve optimization problems. (a) Part of the graph of f(x) = x + 2x…

A: The given function is

Q: If y xy + x² + 1, then when x = 01/1/12 0 - 12/1/20 O nonexistent O -1 O-2 -1 dy d = ? dx

A: we need to find out the derivative of the function at the given value of x.

Q: 6. Gravel is being dumped from a conveyer belt at a rate of 30 meter³/min and it forms a pile in the…

A: Diameter = height(h)radius r = h = 2rVolume of circular cone =

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A: Here And Now,         ..........(1)

Q: Let f(x, y) = x sin(x + y) (a) Calculate the directional derivative of f at the point (1,-1) in the…

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Q: Consider the function f(x) = 3x² - 10x +9, 0≤x≤7.

A: f(x)=3x2−10x+9,0≤x≤7

Q: For the function below, find (a) the critical numbers; (b) the open intervals where the function is…

A: In this question, we will find the critical point , interval where function is increasing or…

Q: Differentiate the given function. 8 (71 + 1/ ) (71²-9) F(t)= 7t =

A: we need to differentiate the given function.

Q: h(x) = 4x x² + 6x + 8

A: h(x)=4xx2+6x+8

Q: Differentiate the function. y = (In(1 + ex))? y' =

A:

Q: dz Find when u = 0, v = 3, if z = sin (xy) + x sin (y), x = 3u² + v², and ди y = 2uv.

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Q: 2. Calculate the Jacobian of the coordinate change (x, y, z) to cylindrical coordinates (r, 0, z).

A: To calculate the Jacobian of the coordinate change  to cylindrical coordinates .

Q: If f(x) = f'(x) = f'(4) = tan x - 5 sec x 3x² tan(x) sec(x) X

A: The Quotient Rule:Use the common derivatives:

Q: Find the upper and lower sums for the region bounded by the graph of the function and the x-axis on…

A: To find the upper and lower sums for the region bounded by the graphof the function and the x-axis…

Q: The following limit results in 0 when you first try to plug in the limit value. 0 Complete the steps…

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Q: Give an example of a rational function f (2) such that lim f(x) = ∞o. 4 Use only the lower-case…

A: In this question, we will find the rational function.

Q: Find the location of the maxima, minima, and saddle points of f(x,y), if any, given the partial…

A: The given first order partial derivatives are

Q: Consider the function F(x, y) = xy2 + 2xy-6y2-8x-12 y + 54. (a) Find the critical points, where Fx…

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Q: Find the critical numbers and the open intervals on which the function is increasing or decreasing.…

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Q: Practice 7: y=x√√x Find an equation of the tangent line to the curve y = 1 + 3x that is parallel to…

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Q: 2. a. C. Determine the critical number(s) for the following functions. f(x) = 17-6x + 12x²…

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Q: Describe verbally the transformations that can be used to obtain the graph of g from the graph of f.…

A: we are given two functions, we need to write down the transformation that f(x) should undergo in…

Q: Express each function as a composition of two functions. (Find f(x) and g(x) such that the given…

A: We have to write the given function as a composition of two functions.

Q: Exponential Growth: a. The table below represents an exponential function. Find the missing values.…

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Q: What is the acceleration of r(t) = (et cos(t), et, t).

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Q: Determine if the geometric series converges or diverges. If it converges, find its sum. 8 1+ + 8 9 2…

A: To determine whether the following geometric series converges or diverges.If it converges, then to…

Q: Find all critical numbers c of f(t) = 3t²/³ +t5/³.

A: f(t)=3t2/3+t5/3

Q: Use the Shell Method to find the volume of the solid generated by revolving the region bounded by…

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Q: Find the inflection points of thefunction f(x) = e(79-x²). INTERMEDIATE WORK f'(x) = f"(x) = On what…

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Q: Graph the function hoo-x-30 0x30 30x50 0.5x-65 i x>50 Choose the correct graph below OA 1530456075…

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Q: Evaluate the limit at -infinity. (If an answer does not exist, enter DNE.) t 4t² + 1 lim t→-∞

A: Consider the limit

Q: 1. Consider the following function, if x # 0 if x = 0 Prove that the function f is differentiable at…

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Q: (f) y = [7+ sec(ax)]2⁰. 120

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Q: Solve the given boundary-value problem. y-10y+25y=0, y(0)=1 y(1)=0

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Q: Consider the following. f(x) = √√49 - x² Find the critical numbers. (Enter your answers as a…

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Q: The curl of the vector function 7 = is: VXU=< 0,

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Q: Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. lim (15 tan…

A: y=limθ→π2−(15tan⁡θ)15cos⁡θ

Q: please show all steps what are 2 critical points of the function: f (x)  =  esin(πx/20) −…

A: Consider the function f (x)  =  esin(πx/20) − cos(πx/20)

Q: 1. Find the volume of the solid determined by x² + y² ≤ zª and z¹ ≤ 1.

A: To find the volume of the solid determined by the inequalities x^2+y^2 ≤ z^4 and z ≤1, set up a…

Q: Find the derivative of the function. y = cos( cos(√sin(tan(7x))) y' =

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Q: Use the quotient rule to find the derivative of -10 sin(x) - 1 6x² +5 You do not need to simplify…

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Q: Find the derivative a. f(x)= 6/(3x2-pi)4 b. f(x)=((3x2-pi x)4

A: (a) given,

Q: What is called a quadratic equation and give 3 examples by calculating its factors with detailed…

A: I have appended the formula used in the solution procedure

Q: Determine whether C(A + B) is defined. If it is defined, express the result as a single matrix; if…

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Q: For the following integral, (a) sketch the corresponding area, (b) approximate the area using the…

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Q: Complete the table. y = f(g(x)) y = (6x - 1)4 u = Need Help? Read It u = g(x) y = f(u) =

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Q: If y = cos² 3x, then =? dy dx dy dx O dy dx dy dx = 6 cos 3x = = -2 cos 3x -6 sin(3x) cos(3x)

A: Given,