Find the dimensions of a rectangle with area 216 m whose perimeter is as small as possible. (If both values are the same number, enter it into both blanks 6. X m (smaller value)

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Q: What is the unit vector oppositely directed to 4?−5?−5??

A: Topic:-  vector algebra

Q: V25x² -69 – dx

A: We will find the integral as following.

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Q: 2. Find the radius of convergence and interval of convergence of the series. (a) (-1)--1 (" – 5)*+1…

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Q: |* (1-x)° dx The solution of the betta function is:- -1 45045

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Q: x²+1, xs1 f (x) dx if f (x) = 2, raluate x> 1 A) 10 20 B 3 12 8 D 3

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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A: Second Derivative Test :   Firstly find critical point of f(x).i.e, f'(x)=0 and find the value of…

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A: At first we want to find radius of the circle.

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Q: 3dt 1. J (2r+8) fr+1 Suv-2+1 ¢v 25x -9 dx 3. 4. V40-4v-v dv

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Q: Using the substitution Z=V x+2, the integral xVx+2 dx is equivalent to | 2°(?+ 2) dz 1 | 22?(z?+2)…

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Q: - ſ csc²e cot êī – 5 cot ê dê

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Q: dy S4ト9-とト」

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Q: Answer the following about the function f (x) = (1/3)x^3 − (1/2)x^2 −2x + 1 a. Find all critical…

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Q: 6)Let f ( x ) = x4 + x3 - 3x2 + 1 a)Find all the hypercritical values. b)Determine the intervals…

A: The given function is f(x) = x4+x3-3x2+1 ............................ (1) We have to a)Find all the…

Q: 4. f(x) = sin xand g(x) = 2x 5. f(x) = x² + cosx and g(x) = 3x + 4 Guide Questions: 1. How did you…

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Q: Directions: In implicit differentiation, we differentiate each side of an equation with wo variables…

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Q: 2Tx [e?n* + 23c] dx

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Q: Find the equation of the tangent to the function f(x) = -4 sin’x at the point where x = (use EXACT…

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Q: coordinates

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Q: 2. The solution to the equation below is x = 2 and x = 5. cos? æ – 7 + 10 = 0 O True O False

A: The given equation is:

Q: 4 5 Replace the letter A in the integral | A(2æ® + 4)* dæ so that the integral evaluates to - (2a® +…

A: Given,            The integral∫A2x6+44dx evaluates to 152x6+45+C.To find : The value of A.

Q: For the graph shown, identify a) the point(s) of inflection and b) the intervals where the function…

A: Given graph:-     To find:- For the graph shown, identify a) the point(s) of inflection and b) the…

Q: How do you take the integral of 2 * sqrt(t^2 + 1) ?

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Q: Find the lengths of the sides of the triangle with the indicated vertices, and determine whether the…

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Q: Suppose the position of a particie is given by parametrc equations x(e) = -3 and y(t) = 2?. (a) Find…

A: The given data is: xt=t3-3yt=2t2  (a) To find the particle's position (x,y) at t=3

Q: 1. Given f(x) S(x) = x² + 4x - 2 and g (x) = 3x – 4 , find the composition of functions for the…

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Q: 3 2 2 3 1, find the matrix B Such that AB = 5 3 4 3 4 2 1 6 1 5 6 4 , If A = 1

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Q: Suppose that fis continuous and that / f(x)dr=4 and / s(x) dr=7, Find / 45 (x) dx A 20 B 28 16 12

A: using property∫acf(x) dx=∫abf(x) dx + ∫bcf(x) dx∫-33f(x)dx +∫36f(x)dx=∫-36f(x) dx4 + ∫36f(x)dx…

Q: A bacteria culture is known to grow at a rate proportional to the amount present. After 60 minutes,…

A: We will find the number of strands of the bacteria originally in the culture as following. After 60…

Q: Which of the following is not correct? 4dx 4dx A Jo Jx(x+6) = lim o Vx(x+6) C+ .3 dx .3 dx B h…

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Q: Using the substitution z=Vx+2, the integral xyx+2 dr is equivalent to (A) | 222(z2- 2) dz .7 (в |…

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Q: lim f(x) = c lim f(x) = 00 lim f(x) = 0+ lim f(x) = 0- x-1+ X-1- f(0) = 0,f(-1) = -f(-2) = -

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Q: 2x + 5x 1. Ar + Ba + Cz² + D¤ Consider the function f(x) = An antiderivative of f(x) is F(z) where A…

A: Answer is solved in step 2 using integration.

Q: S (sech*y – sec®y) dy

A: I =∫ (sech4y -sec6y) dyI=∫ sech4y -∫ sec6y dyI=∫ sech2y (1-tanh2y) dy       -∫ sec2y (1+tan2y)2…

Q: 2. The function g(x) is defined for -3Sx5 3. The behaviour of g'(x) and g"(x) is given below.…

A: A)-3<x<-2, g'(x)<0and-2<x<1, g'(x)>0Function decreases over (-3, -2) andincreases…

Q: How do you take the integral of 2 * sqrt((t^2 + 1)) ? Can you label notes on each step? I can't see…

A: We will solve this question using integration by parts.

Q: 1. Find the radius of convergence and interval of convergence of the series. (a) (-1)"(n+1)"a²" n=1

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Q: Given f''(x) = 4x – 5 and f'(– 3) = 3 and f( – 3) = 6. Find f'(x) = and find f(3)

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Q: if xo = 2, x1= 3 and x2 = 4 the second degree %3D %3D polynomial for f(x) = ! using Lagrange %3D…

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Q: complete and detailed using techniques of variation

A: Given,            ∫dy1+y+13