Given the points A(4, 2) and B(3, −1).  1. Find the components of vector AB and draw its position representation. 2. Find the unit vector in the same direction as vector AB. 3. Find its direction angle (radians).

Q: Using differentials, solve for the approximate change in the hypotenuse of a right triangle if the…

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Q: 9. y(cos³x) (cos²2y)

A: We are asked to find the solution of the differential equation

Q: Explain why the function is discontinuous at the given number a. (Select all that apply.) (x+5…

A: Given function,f(x)=x+5if x≤-12xif x>-1

Q: 20. If you use the ratio test on the divergent series $ Σ2-1 =1 inequalities will result? n+4 A.…

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Q: Suppose you wish to retire at the age of 65 with $90,000 in savings. Determine your monthly payment…

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Q: Methods by substitution (2x+1) dx - (x+3y+2)dy =0

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Q: Starting with 2 = A + B₁ show that 2 x 2 = 0 ledd's to A×B = - B × A

A: Given query is to find prove above vector operation.

Q: how did you break up 3x-2 into 3/8(8x+4)-7/2? is there a method or formula to follow into deciding…

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Q: 8. X lim 2 xxx +8x

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Q: Determine whether the given relation is an implicit solution to the given differential equation.…

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Q: Let P be a point on the parabola y = 4x2, and let Q be the point where the perpendicular bisector of…

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Q: Show that f is continuous on (-infinity, +infinity) f(x)= { 1- x2 , if x less than or equal to 1…

A: A function f(x) is said to be continuous at x=a if limx→a-f(x)=limx→a+f(x)=f(a).Also we know that a…

Q: Eliminate the arbitrary constants y = -x (c₁ cos 2x + C₂ sin 2x)

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Q: Find the cross product a x b. a =j+9k, b = 5i - j + 2k

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Q: x² + y² = 8 y = x + 4

A: Solution

Q: Find the Taylor polynomials of orders n = 0. 1, 2, 3. and 4 about o and then find the nth Taylor…

A: Please see the below picture for detailed solution.

Q: Write an equation for line L in point-slope form and slope-intercept form. L is perpendicular to y =…

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Q: (x-p)(x-q)² (x-r) If p, q, and r are real numbers that may or may not be equal, the graph of the…

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Q: a) Find f'(x) using the definition of the derivative: f(x) = √7 - 20x f'(x) = b) State the domain of…

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Q: If f(x) = 3x² − 3x + 5, find ƒ'( – 5). Use this to find the equation of the tangent line to the…

A: Equation of tangent line

Q: determine whether the following function y=c₁x +₂¹³ +21²²-2re* is a solution to the differential…

A: We can solve this as follows:

Q: Using differentials, solve for the approximate change in the hypotenuse of a right triangle if the…

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Q: Write an equation for the polynomial graphed below y(x) = 4 3 2 1 1 2 3 Submit Question H a

A: We have given graph of the polynomial  From given graph  Zeros : x=-4,-2,3,4 y-intercept : y=2 Let,…

Q: π/2 cos(y) 1/6 So π/6 -y ㅠ y sin (y+z)dz dx dy

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Q: Let f be a differentiable function such that f (2) = 2 and f' (2) = 5. If g(x) = x³ f (x), what is…

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Q: Find the solution of the following DE. Show your complete solution. 1. y' 2x v+x²y ; y(0) = 2

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Q: 56. s 1 √x² +9 dx

A: See this solution in below.

Q: 2. Determine all the combinations of cross products between the standard unit vectors i, j, and k.

A: Cross product between standard vectors follows the clock wise direction as shown in the diagram.

Q: On a sketch of y=ex, represent the left Riemann sum with n=2 approximating ∫2 3 e^x dx. Write out…

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Q: Write down a continuous function f(x) with maximal value M = 3 and minimal value m = -2 on the…

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Q: Find the average rate of change of the function f(x) = x² + 9x from x₁ =2 to x₂ = 5. The average…

A: As we know that; The average rate of change of the function fx between the interval x1≤x≤x2 is given…

Q: 4. Determine the particular solution of the following differential equation: y'=5xy-2x Where: x=0;…

A: Topic = Differential equation

Q: Q1. Evaluate feax Sinbx dx.

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Q: Use sigma notation to write the Maclaurin series for the function 131n(1 + 2) ΣΕ Κ

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Q: Given y = -3x^2 + bx + c , find b so the graph  could be in quadrant 2.

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Q: x + 2z = 1 2y-z = 8 xyz = 0

A: Note-there is no rule such that type written solution only, so here i will solve question hand…

Q: Given the differential equation (4x²+ y² dx+x (x−2ydy=0

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Q: 17 0 (Use a comma to separate answers as needed.) (i) What are the y-intercept(s)? X= y= (Use a…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Evaluate [ cos²x = 2

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Q: J 3x - 2 4x² + 4x + 17 dr

A: Breaking the numerator is the key here. After that, break the given function into two parts and then…

Q: A loan shark lends you $90 at 2% compound interest per week (this is a weekly, not an annual rate).…

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Q: Use the graphs shown in the figure below. All have the form f(x) = ab. Which graph has the largest…

A: Given graph, Given function, f(x)=abx

Q: Find the derivatives using the of limits (4-step Rule). Show each step from step 1 to 4. C…

A: -41-3x2' =-411-3x2' =-41-3x-2' =-21-3x31-3x' =-4-21-3x3-3=-241-3x3

Q: Prove: २ tan² x sin²x = tan ²x -sin ²³ x ·

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Q: 7. Do Exercise 5 by another method. 8. Do Exercise 6 by another method.

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Q: 2. y' = 2y4+x4 xya

A: We can solve this as follows:

Q: 22. Approximate the curve cos (3x) + 2 with a Maclaurin polynomial. A. 2-(3x)² +2+ (3x)² +2 + 4…

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Q: -5 -4 -3 -2 -1 0-3 0-2 0-1 Do 01 5+ 4 3- 00 3 04 1 -1 -2+ -4+ -5+ Select all the x-values at which…

A: A function is not differentiable at x = k if  the function satisfies  any of the following…

Q: 6) Find all the zeros of f(x)=x²-3x²+4x-2 and write f(x) in factored form

A: Given query is to find the zeros and write in factored form.

Q: Let A be a matrix, and let x and y be vectors such that neither is a scalar multiple of the other…

A: Given: Ax=y and Ay=x+2y.We need to find the value of a and b such that A5x=ax+by.