Identify the type of solution for the problem and solve for the general equation

Q: Use the properties of the derivative to find the following. r(t) = ti + 5tj + t²k, u(t) = 4ti + t²j…

A: This question is based on dot product of two vector. (a i + b j).(c i + d j) = ac + bd

Q: Find three positive numbers x, y, and z that satisfy the given conditions. The sum is 40 and P =…

A: Given that    Three positive numbers x,y and z                The sum of these numbers is 40.…

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = (1, 5, 5)

A: Follow the procedure given below.

Q: The holes cut in a roof for vent pipes require elliptical templates. A formula for determining the…

A: We need to find length and width.

Q: ∞ Determine whether the series (-1)-In -1/3 is absolutely convergent, conditionally conver- n=1

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Q: Find the real roots of the equation B 244

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Q: (a) Determine whether the series (b) Determine whether the series ∞ n=1 ∞ n=1 n+1 n³ +3 is…

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Q: Find the minimum distance from the point to the plane x - y + z = 6. (Hint: To simplify the…

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Q: part, and you will not be able to come back to the skipped part. Tutorial Exercise Solve the…

A: The given differential equation is;  y''+3y'+2y=1/(8+ex).

Q: A function f is said to have a removable discontinuity at a if: 1. f is either not defined or not…

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Q: Use the substitution u=x2+4 to evaluate the indefinite integral below. 2x(x2+4)8

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Q: Please

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Q: (a) Area = ſ dx dy (b) Area = = [[ JJ dy dy dx

A: Follow the procedure given below.

Q: Question 4 An artist has decided to finish their piece of artwork by balancing it on a fulcrum and…

A: Given that y=sinπx+4bounded by x=0,x=2 and y=0Solutiuon :centroid x¯…

Q: Find two positive real numbers x and y such that their product is 2450 and x + 2y is as small as p…

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Q: Evaluate the integral of x cos 2x dx with limits form 0 to pi/2. (A) -3/4 B 0.75 C -0.5 D 1/2

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Q: Find aw/as and aw/at using the appropriate Chain Rule. Function Values w = sin(2x + 3y) x = s+t,…

A: We can answer both the answer as below.

Q: 1 g(x)= {x-1 if x > 0 |x² −1 if x≤0

A: The given function, gx=1x-1if x>0x2-1if x≤0

Q: Find an equation of the tangent plane to the surface at the given point. (2,0,0) g(x, y) = arctan…

A: Answer and explanation is given below...

Q: Identify any extrema of the function by recognizing its given form or its form after completing the…

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Q: Find f(x+h)-f(x)/h for the given function . f(x)=x2+8x

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Q: (-tanx) ydx + Inlexy cos x| dy = 0

A: We need to find out the general solution of the given differential equation.

Q: Write an equation for the function graphed below 5+ 4 3 2 1 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 y = -5+ 1…

A: topic- graph of a function

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

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Q: What will go wrong if we choose u = x²? Notice: in that case, we will also be choosing du = ln x dx.

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: For the function f(x,y,z) = x rr fy 11 he e = 11 f₂ = N fyz 10 8z+1 -9 8z+1 (9y-10x)8 (8z+1)² 11 72…

A: The given function is;  f(x,y,z)=(10x-9y) /(8z+1).

Q: Sketch the region R whose area is given by the iterated integral. 8 8-x [*ª [* dy dx + £® ® - * 8 y…

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Q: Let f(t)= F"(t), with F(t) = 5t2 +t, and let a = 4 and b=7. Write the integral f f(t) dt and…

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Q: If you invest $5000 compounded continuously at 4% p.a. how much will this investment be worth in 5…

A: The initial amount P=$5000 Rate of interest r=4%=4100=0.04 p.a. The time period t = 5 years

Q: The given family of functions is the general solution of the differential equation on the indicated…

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Q: - The complementary function is १ex . Ус where C₁, C₂, C3, C4 си the particular Solution se = c₁ex +…

A: This is a problem of ODE. Please follow the procedure given below.

Q: Evaluate the integral. X √ ² ₁x + (x + 16y) dy

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Q: 15) I What is the average rate of change of f(x) = from x = -2 tox = 4? x-s X+3 b 24 7 M C. d. 25 21…

A: We know that the expression for the average rate of change between the interval x2≤x≤x1 is: Average…

Q: - (D² +8D³² +16) y = _ sinx Ans: Y=as2x+ C₂ Sin2x + C3 Xcos2x + (4x sin2x - 1 9

A: The solution is given below

Q: Analyze the following graph of f'(x). Select all of the intervals over which f(x) is concave down.…

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Q: What is the maximum value of the function h(x) = 10x =—= 22² x² on the interval 0≤x≤ 40 and for what…

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Q: Find the area bounded by the given curves. Use vertical strip x² = y - 1 and x = y - 3

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Q: ((x)/)6 (1) (e) f(g(x)) ((7-))* (P)

A: Given;  f(x)=2x3 and g(x)=4x+5.

Q: A population of rabbits oscillates 29 above and below an average of 75 during the year, hitting the…

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Q: (2x +3y) dx + (y +2) dy = 0

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Q: Identify any extrema of the function by recognizing its given form or its form after completing the…

A: The given function is fx,y=x2+y2+6x-18y+3

Q: Evaluate the iterated integral. π/4 ** ['y cos(x) dy dx

A: Please see the below picture for detailed solution.

Q: Vf(1, 3) =

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Q: The length of a rectangle is three times its width. If the area of the rectangle is 108 yd², find…

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Q: Write the expression in algebraic form. [Hint: Sketch a right triangle, as demonstrated In Example…

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Q: Determine csc(x) + cot (x) if tan x + sec(x) = 22/7. 27/12; 29/15; 24/18; 23/11

A: We can answer the question by finding the correct option as below.

Q: *T/2 10 cos(0) r dr de

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Q: Evaluate the iterated integral. 2y 1²1,²% (10 + 8x² + 6y²) dx d 0 ly

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Q: Find the gradient of the function at the given point. Function g(x, y) = ye-x Vg(0, 9) = Point (0,9)…

A: Given function: g(x,y)=ye-x

Q: A force of 660 newtons stretches a spring 3 meters. A mass of 55 kilograms is attached to the end of…

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