DIRECTIONS. Indicate the degree and determine the solution of the following equations. 2.  (3x² - 2xy + 3y2)dx = 4xy dy

Q: 15. Evaluate each expression using the given table of values: -2 -1 1 f(x) 1 0 -2 1 2 g(x) -1 b.…

A: To use the table of values for finding the values of given function.

Q: aluate the integral. [29 tan 29 tan 5x sec 4x dx

A: The given integral is  ∫29tan5xsec4xdx

Q: Please have a systematic way of solution (Question-Solution-Final Answer-Conclusion format) E.…

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Q: Problem 1. Is the following true or false? Justify your choice. 4x (x − 1)(x + 3)' Bx + C x + 3 To…

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Q: theater finds that there is a correlation between the number of ice cream flavors offered at its…

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Q: Find the equation of the plane through the point (3, -3,0) that is tangent to the surface xy² + 3ye²…

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Q: You are taking a multiple-choice test that has ten questions. Each of the questions has four answer…

A: There are 10 questions in the test and each question has 4 answer choices with one correct answer.

Q: Let F(x)=f(f(x))=f(f(x)) and G(x)= (F(x))2 and suppose that f(6)=7, f(7)=2, f′(7)=3 ,f′(6)=8 Find…

A: As we know that for composition of function F(x)=ff(x), F'(x)=f'f(x)×f'(x)

Q: Consider the following limit statement: lim (9x-3) 15 x → 2 Find the corresponding value of 6 when &…

A: givenlimx→39x-3=15

Q: f(x) = b сos(x) - 2 3x² - ax + b 2x - 4a { x ≤ 1 ax+b 1 2

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Q: FIND F'(x) F(x) = 2 tanx 1+cosx

A: To differentiate the given function.

Q: Let f(x) = √√4x² 4x² + 3x + 5

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Q: (a) Find the distance from P1 = 1 - 2, - 32 to P2 = 13, - 52.(b) What is the midpoint of the line…

A: Given, P1=-2, -3 and P2=3, -5

Q: 6 5 4 3 2 I 1 it y = f(x) X

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Q: Find the total area bounded by the graphs of f(x) = 3x³ - x² - 10x and g(x) = -x²+2x. 32 units² O 8…

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Q: Find the implicit equation of the tangent plane to z = ln(x² + 1) + y² at the point (0, 5, 25).

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Q: According to one model that takes into account air resistance, the acceleration a(t) in m/s" of a…

A: Here is the solution:

Q: Evaluate the expression.

A: Given: The given expression is: C15·C27C312 Formula Used: Crn = n!r!(n-r)!

Q: parts remaining Evaluate using integration by parts or substitution. Check by differentiating. (3x²…

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Q: Find the area of the region bounded by the curves y = x² 3 x - 3x and y= 3 x 1 - 3x on the interval…

A: Let's find area of region bounded by two curves.

Q: Constructing an Open Box An open box with a square baseis required to have a volume of 10 cubic…

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

Q: lim 1 - cos(sin(³-1)) 73 - 1

A: As per the instruction, we will be answering the first question. The graph of y=1-cossinx3-1x3-1.

Q: Find the derivative of the function r = sin(0³) cos(30). dr do

A: Solution

Q: Find an equation for the tangent plane and parametric equations for the normal line to the surface…

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Q: Area of a Rectangle A rectangle has one vertex in quadrant Ion the graph of y = 10 - x2 , another at…

A: A vertex of rectangle lies on the following: y=10-x2 Since the area of rectangle is maximized when…

Q: Evaluate lim 1 1 x 2 X-2 X-2 direct substitution. 1 1 X 2 O lim X-2 X-2 1 1 X 2 O lim X-2 X-2 O lim…

A: The objective of the question is evaluate the limit and choose the correct option.

Q: A car has 12,500 miles on its odometer. Say the car is driven anaverage of 40 miles per day. Choose…

A: Given data:- A car has 12500 miles on its odometer Car is driven an average of 40 miles per day N is…

Q: Elimination of Arbitrary Contants 1. y = peax cosbx + yeax sin bx 2. y = c₁x + c₂ex ; a and b are…

A: we need to eliminate the arbitrary constants C1 and C2

Q: 3. Elimination of Arbitrary Contants 1. y = peax cosbx + peax sin bx 2. y = C₁x + c₂ex ; a and b are…

A: Here we have to eliminate the arbitrary constants of the equation y=ϕeaxcosbx+ψeaxsinbx…

Q: The variable interest rate on a student loan changes eachJuly 1 based on the bank prime loan rate.…

A: Given for the years 1992–2007, The rate can be approximated by the model r(x)=−0.115x2+1.183x+5.623…

Q: II. Give the indicated derivative 1) find the 27th derivative of cos x

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Q: The limit lim h→0 f(x) a = = In(e +h)-1 h represents f'(a) for some function f and some number a.…

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Q: 1. y' + ytanx = COSX; y(x) = (x + c)cosx; y(π) = 0

A: y'+ytanx=cosxy(π)=0proove that  solution isy(x)=(x+c)cosx

Q: Please have a systematic way of solution (Question-Solution-Final Answer-Conclusion format) E.…

A: Solution

Q: Compute the directional derivative of the following function at the given point P in the direction…

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Q: Evaluate the limit If the limit does not exist enter DNE. Limit Number = lim x 6 x2 x-6 6 x

A: To evaluate the following limit.If the limit does not exist then to enter DNE.limx→6 x-6x2-6x

Q: 13. The graph of the first derivative f'(x) of a function is shown. Identify the graph of f. N

A: Given query is to find the the graph of the function from the derivative graph.

Q: Express the function h(x) = 5log(x² + 6) the form fog. If f(x) = 5log(x), find the function g(x)

A: We can find the function g(x) from the given composite function in the below steps.

Q: Find the average rate of change of f1x2 = 8x2 - x:(a) From 1 to 2 (b) From 0 to 1 (c) From 2 to 4

A: Given: Given expression: f(x) = 8x2-x Formula Used: The Average rate of change ARC = f(b)-f(a)b-a

Q: Find the interval of convergence of the following series Σ(-1)₂(x - 2)n n5n n=1

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Q: The graph of f(x) below has a hole when x=_ and y=

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Q: Explain how to find a particular term in a binomial expansion without having to write out the entire…

A: Binomial expansion is to expand and write the terms which are equal to the natural number exponent…

Q: If f(x, y, z) = 3xy + z² and u is the unit vector in the direction of (3, -3, -4), then the…

A: This question can be solved using the concept of derivatives and vector.

Q: Find the numbers at which g is not continuous. Justify using the definition of continuity. x+2 if x…

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Q: Which one of the following could be the graph of the curve given parametrically by when the graphs…

A: Graph 4  could be the graph of the given parametrically  graph

Q: At t = 0, a train approaching a station begins decelerating from a speed of 104 mi/hr according to…

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Q: Find parametric equations representing the line segment joining P(-3, 2) to Q(2, -1) as (x(t),…

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Q: A car sharing service offers a membership plan with a $30 per month fee that includes 10 hours and…

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Q: In problems 14-16, use the properties of definite integrals to support your answer. Be specific.…

A: Given, ∫26f(x)dx=9⇒f(6)-f(2)=9…

Q: Find the exact length of the curve. 1 y² = 16(x + 1)³, 0≤x≤ 3, y>0 109/109 (217 217 (21717 X

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