Find the dimensions of a rectangle (in m) with area 216 m2 whose perimeter is as small as possible. (Enter the dimensions as a comma separated list.) m Need Help? Read It

Q: Find the values of a and b such that f is differentiable at x = 3

A: Given,            The function is fx=ax+bx≤32x1-1x>3To find : Find the values of a and b such…

Q: Part 3. Provide solution in finding the derivatives of the given function 1. y= 4x5-2x + 3x- 10 2. y…

A: Let's find.

Q: Simplify f and find any vertical asymptotes of f. x²(x+8) f (x)= x²+ 8x

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Q: Free-Falling Object In Exercises 37 and 38, use the position function s(t) = -4.9f + 250, which…

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Q: Show that for x 2 1, cosh (cosh° 3x – sinh° 3x) = In(x+Vx² -1). (b)

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Q: A. Integration By Parts 1. ſx5Vx3 + 1 dx 2. S/* x sin 2x dx 3. S- x³ex? -dx (x2+1)2

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Q: Question Is S (÷x² + 5x + C ) dx = Зх + 5 сorrect? CLAIM EVIDENCE REASONING

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Q: Format View Help File Edit Format View Help Ln 57, Col 1 100% Windows (CRLF) UTF-8 Consider the…

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Q: Give the curve r=3 cos 0 a) Find the points on the given curve r = 3 cos 0 where the tangent line is…

A: θ r=3 cosθ 0 3 π4 32 π2 0 3π4 -32 π -3 5π4 -32 3π2 0 7π4 32 2π 3

Q: rational functions solve suppose it costs C dollars ( in billions) to build X miles of a wall…

A: A)C(x)=0.425 x1954-xwhere, x is the miles of the wall.cost to build 1000 miles of…

Q: Find the area bounded by these curves. (All choices are in sq. units) y = x 4x +y = 12

A: Here, the is a line passing through the origin. And,  4x+y2=12⇒4x=-y2+12⇒x=-14(y-0)2+3 which is a…

Q: Answer the following about the function F(x)=x^4-24x^2+700. Justify all your answers. A. Find all…

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Q: 1. Given: 7- 4r S(x) (z+2)² ' with f'(x) = (z + 8)(z= 2) and f"(z) = 8(7x – 4) (x+2)³ (z+ 2)* * e.…

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Q: 10. * -1 x CSc

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Q: The dimensions ofavectangubr region are varging with the bimeltyacCording W-zt+6cm/see where Listhe…

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Q: Find the limit. (If you need to use o or -oo, enter INFINITY or -INFINITY, respectively. Round your…

A: lim  ln(x-2) x--2+ here we can direct apply limit  ln(2-2) = ln0 =  INFINITY

Q: one-sided limit (if it exists). 72. lim

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Q: 5. Use L'Hospital's rule to compute the following limits (a) lim a In(x) (b) lim sin(z) (c) lim…

A: Here are the solutions: We will use L'Hospital rule and differentiate the numerator and denominator…

Q: Consider the following. u = -6i - 4j - 2k, v = 4j + 4k (a) Find the projection of u onto v. (b) Find…

A: Projection

Q: A ball is launched straight up in the air from a height of 6 feet. Its velocity (feet/second) t…

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Q: 37 Let (): (Give an exact answer. Use symbolic notation and fractions where needed.) <1< 2x and cos…

A: cos(t)=49    and    3π2&lt;t&lt;2π We need find the value of cost2 using half-angle formula.

Q: Qz IF A-(-2 4) B=(% 4) 2 3 -2 4 Prove! CA *B)*C A*(BaC)

A: Here, the given matrices are: A=-24, B=5104, C=23-1-241

Q: х3 — 4х? 8(7x – 4) (x + 2)* x(х + 8)(х — 2) | Given: f (x) : with f'(x) ,аnd f" (x) - %3D (x + 2)2…

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Q: Write the form of the partial fraction decomposition of the rational expression. бх — 1 († – x)x A В…

A: (6x-1)/x(x-4) it is very simple because in numerator there us multiplication given so A/x + B/(x-4)…

Q: 6. gx) VX- 3 at x = 4 三 7 g(x) at X = 8 三 e1 gCX)= n4ーメ at x =0

A: Given

Q: Find the volume of the solid of revolution if a quarter of an ellipse in the first quadrant with…

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Q: - The rate of change of the monthly profit for a new company is given by the function P'(t) = 200VE…

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Q: Referring to the graph above, which of the following statements is correct: 1. f″(x) 0 for all x

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Q: Flnd * |(sin 5x cos 3x + cos 5x sin 3x) dx cos 8x cos 3x + 3 cos5x – + c 8 + c Option 3 Option 2 cos…

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Q: A farmer's house sits 3 miles due south of a river. The diagram below shows the path that the farmer…

A: First assume a distance as x then make the relation between total  distance  and x.. And then for…

Q: Given the function f(x) = (÷) (a) Find a power-series representation for f(x). Σ п(п +1) (п + 2)!…

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Q: dx 5 x + 2y 2 dt dy 3 ーX 4 – 2y dt

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Q: 7. * In [In (In æ)]

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Q: Find the volume of the solid formed by revolving the region bounded by the curves x=2√y, y=0, and…

A: The graph is shown below, where the chex region represent the required volume to find.

Q: /| J. Let J = xy dA where D is 2 %3D D the region bounded by the x-axis, .3 y = x' and x = 2

A: Intersection points:y=x3, x=2, y=00=x3(0, 0)y=23 =8(2, 8)

Q: Let i = (6, – 6, 1) and v = (– 5, 5, – 6). %3D Compute the following: i · i = i. i = - 6(ü - i) = (–…

A: To evaluate the given dot product of vectors u and v.

Q: If f (x,y) = In(x² + y²), then fx(x,y) + fyy(x, y) is: а. 0 x+y b. x2+y2 2х+2у с. x²+y2 d. Undefined

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Q: Find the net area and the area of the region bounded by y 2cosx and the x-axis between x = - and x =…

A: Use the integration to find the net area and area bounded by the given region.

Q: Evaluate the limit below. - 2x2 + 13x – 21 lim x→3 х — 3 -

A: limx→3-2x2+13x-21x-3apply L hospital rulelimx→3-2(2)x+131limx→3-4x+13

Q: 5 dx J 125x2-9 5. 4t.a-2t

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Q: sec*(x) dx. Vtan(x) a) Vtan(x)[5 + sec²(x)] b) V sec(x)[5 + tan² (x)] c) V tan(x)[6 + tan? (x)] d)…

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Q: The equation 0-10x+5= 0 does not have a root in (0, 1) Select one True False

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Q: Finding a Limit In Exercises 11–28, find the limit. Use a graphing utility to verify your result.…

A: LetL=limx→ 0x+1-13xlimx→ac·fx=c·limx→afxL=13·limx→ 0x+1-1xRationalise the numeratorL=13·limx→…

Q: Find the area of the portion of the surface z=f(x,y) = x^2+ y^2 that lies below the plane z = 9.

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Q: n evergreen nursery usually sells a certain shrub after 7 years of growth and shaping. The growth…

A: Given query is to find the solution of the differential equation.

Q: Solve the system of linear equations and check any solution algebraically. 5x - 3y + 2z = 3 2x + 4y…

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Q: 2. Find the volume oF solid obt ained by revolving the region bounded by the about the x- axis the…

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Q: Find the Volume y=0, y= 1/x, x=1, x=4 revolving at the x-axis

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Q: Given are two points [1,3] and (6, –1] in the plane. Which equation of the form a ·z + b•y+c=0…

A: (y-y1)/(y2 -y1) = (x-x1)/(x2-x1) (x1,y1 ) = (1,3) (x2,y2 ) =(6,-1) (y-3)/(-1-3) = (x-1)/(6-1)…

Q: The population of an unknown bacteria in an experimental culture is estimated by the population…

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