√√√x if x<0 Let f(x)=₂x if 0≤x≤1 2x-x² if x>1

Q: Find the relative extreme values of p(x) = 20 5 - 3x3

A: Here we have to find the relative extreme values.

Q: Solve the differential equation. 8. x ( 3xy – 4y^3 + 6) dx + (x^3 – 6x^2y^2 – 1) dy = 0

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Q: Evaluate ffz + 3y - x^2 ds where S is the portion of z=2-3y+x^2 that lies over the triangle in the…

A: To find the value of given fds over given region.

Q: 1. Find the volumes of the solids generated by revolving the regions bounded by the lines and curves…

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Q: Q.2)(A) Determine of each point convergens or diverges: R sinhn (4) Στη?)coshn ΑΞΟ (S) Σ ΑΣΘ ((Inn"…

A: Given

Q: Solve the differential equation. 11.    ( 2xy – tan y) dx + (x2 – xsec^2y) dy = 0

A: The given differential equation is; (2xy-tany)dx+(x2-xsec2y)dy=0.

Q: Use the ratio test to determine whether the series converges. If the test is inconclusive, then say…

A: We have to check series is convergence or divergence by ratio test

Q: V. A hemispherical basin of radius 4 ft contains liquid to a depth of 3 ft. If the liquid weighs 48…

A: This is a problem related to pumping volume of the spherical basin to the 3 ft above the container.…

Q: Lea With reference to the activity in learning task # 3, find the derivatives of the following…

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Q: 51 b. Determine the gradient of the following function at Po h(x, y, z) cos xy + e + ln zx, Po(1, 0,…

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Q: A research lab recorded the decay of a radioactive substance. The data table shows the amount of the…

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Q: Find f'(a) using the definition of the derivative at a point for: f(x). 1 = √x at a = 4.

A: Find derivative using  definition of f(x)=1x at a=4

Q: The Summation means that we take 2 the sum of 1²+3 as i goes from 6 to 8 { li i=6 (143) =…

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Q: What is the degree of the following homogeneous function? * f(x, y) = On On-1 On-2 On-3 = xn +…

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Q: f(x) = (2x - 3, if x = 2 # 3, if x = 2 12x 3,1

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Q: A plane Π2 intersects Π1: 4x − 2y + 7z − 3 = 0 at right angles. Two points lie on Π2: A (3, 2, 0)…

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Q: olve the following exponential equation algebraically. 3(2-1) = 215 press you answer to the nearest…

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Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…

A: Formula:- Volume of Parallelepiped = [u v w]

Q: Translate each graph as specified below. (a) The graph of y=f(x) is shown. Translate it to get the…

A: We are asked to translate the given graph.

Q: Correct the answer Find the median for the following numbers: (21, 32,29, 8, 18, 3, 25) A-8 B-7 C-9…

A: To find the median of given set of numbers.

Q: 9. [ 2x + y cos (xy)] dx + x cos (xy) dy = 0

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Q: b. S sin (3x) cos¹ (3x) dx

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Q: For second-order differential equations that cannot be solved by algebraic methods, the…

A: For second order differential equations that cannot be solved be algebraic methods, the leibniz -…

Q: The height of each rectangle is given by the value of the function, f(x) = 5x − x2, at the…

A: Explained below

Q: Separable DE) y'ln² y + y√√x=0 y(0) = e

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Q: Question 14 If z= f(t); u = g(x); x = h(z), which of the following is/are correct? du du dr dz (a)…

A: To find out the correct option.

Q: e) f(x)=tan(cos¹.x) () COS X [+sil x h) y = 2

A: Given

Q: Suppose you are asked to list, in order of preference, the 3 best movies you have seen this year. If…

A: Let's solve number of ways.

Q: y = x³ + 1 (x (x² 2 3 x + 3 -1 - 2x + 1)

A: The given function,      y=x3+1x3+3x2-2x-1+1

Q: да Given zTan¯¹ (x + y) — ln [1 + (x + y)²] = 5%, what is ду -1 2-2x-2y none of the choices 2- 2x +…

A: ∂∂xtan-1x=11+x2 Note : As per our Guidelines , we can solve first question. Please repost remaining…

Q: In (x-2) sketching y determine ex² he intersection of the curve and the orizontal asymptote. None of…

A: According to our company's guidelines I can only answer first question since you have asked multiple…

Q: 8. The polynomials x - 1, (x - 1)2, and (x - 1)³ span R3[r]. 9. If S and T are finite spanning sets…

A: Given

Q: d) y = 21+1 31-2

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Q: Which graph represents two functions that are decreasing on all points across the domain that is…

A: To find out the graph in which two functions are decreasing in the domain common to both.

Q: f(x,y)= exsin (y), fx(x,y)

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Q: b. If F'(x) = f(x) then [f(x) dx = F(x) + C

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Q: 20- 18 16- 14- 12 10 Co 8 6 4 2 1 Estimate the instantaneous rate of change at x = 1

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Q: Find a value of n such that y= x" e satisfies the equation xy' = (x-6)- y. (Use symbolic notation…

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Q: ту 3) 2xydy = (x3 +y=) ax

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Q: 2. f(x) = 1 x²-1

A: We have f(x) =1x2-1

Q: In (x-2)² In sketching y determine the intersection of the curve and the horizontal asymptote. None…

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Q: (C): Find representative Fraction scale (R.F) from verbal statement of (6 inch to 1 mile) (12mile to…

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Q: Use the definition of derivative to find = f'(x). f(x) = for 1 3x

A: Given f(x)=13xf'(x)=limh→0f(x+h)-f(x)h=limh→0(13(x+h))-13xh=limh→013x+3h-13xh

Q: Find the minimum value of the following function: f(x,y,z) = x² + 2y² + z² - 2xy - 2y + 5  using…

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Q: Given x = 5t - 5 and y = 25 sin t dy da t-0 (ii) dy da 2 t-0

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Q: 6X-1 4X+1 X+7< 6 OX<-89/2 (-∞, - 89/2) O X<- 89 (00,- 89) O X<-2/89 (-∞, -2/89) O X<∞ (89/2, ∞) 8

A: x+7&lt;6x-14-4x+16x+7&lt;6(6x-1)-4(4x+1)4×6x+7&lt;36x-6-16x-424x+7&lt;20x-1024Multiply 24 on both…

Q: xsin (y) + ycos(x) = 1

A: To find the derivatives of the given functions.

Q: Find an equation for the line that passes through the points (6,-6) and (-4,-4)

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Q: Q.2)(A) Determine (215) ² Σ (5)(2+1) of each point convergens or diverges: 13.0

A: Given

Q: Question 17 D, (cos(sin x)) = O-sin(cos z) - sin + cos z COS I - sin(sin z) O sin(sin x)

A: