Decompose v into two vectors Vị and v2, where vi is parallel to w and v2 is orthogonal to w. v - -2i - 3j, w = -2i +j %3D V1 16 i- V1 o in

Q: = e3 + C is the general solution to the differential equation: y' = 3y. Select one: O True O False

A: We need to choose correct option.

Q: Using appropriate substitution, sin³ (3x)cos*(3x)dx is equal to -cos"(3x) + cos"(3x) + c - cos (3x)…

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Q: x = -1 x = 1 For what value of c is the function f (x) = continuous at x = -1? 12 –1 (x+1)(x-3)…

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Q: Use a right triangle to write the expression as an algebraic expression. Assume that x is positive…

A: see below the answer and calculation

Q: 20 of 21 What is the average rate of change of y with respect to x over the interval -5, –2] for the…

A: topic- average rate of change of function over interval

Q: For the differential equation (x² – 3)y" + (x+ V3)y' + y = 0, singular point is a regular X=9 x=3…

A: Given

Q: Indicate a general rule for the nth term of the sequence when a, = 2 and r = a, = (/2)(5y* a, =…

A: Given query is to find the nth term of the sequence.

Q: Compute the partial derivatives: 5x dz dz

A: Given query is to find indicated derivative.

Q: The terms of a series are defined recursively by the equations az = 5 5n + 2. an. an+1 4n + 11…

A: Here, the given series has: a1=5, an+1=5n+24n+11an

Q: x2-16 x - 16 Let f(x) = (a) Calculate f(x) for each value of x in the following table. (b) Make a…

A: This question can be solved using the concept of limits.

Q: 10 8 Consider the function f(æ) Let F(x) be the antiderivative of f(x) with F(1) = 0. Then F(x) :

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Q: a) [*. : Determine whether the series 1 Σ (2n – 1)4 n =1 is convergent or divergent.

A: To determine whether the given series is convergent or divergent

Q: dy a. Use implicit differentiation to find dx dy %3D dx b. Find the slope of the curve at the given…

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Q: - f(æ) = Where is %3D discontinuous? x2 + 3x – 18 - o f(x) is continuous everwhere O 3 O-3 and 6 O-6…

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Q: Question 3 1-. a) [. following series -): : Determine whether the (-1)"4"-1 32n+1n n=1 is convergent…

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Q: A piecewise function is given. Use the properties of limits to find the indica fix) if x 3 5. if x-3…

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Q: b) sin(xy) = sin(x) + sin(y)

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Q: Find the length of the curve 7(t) = (4 cos(3t), 4 sin(3t), 4t) for – 4 <t < 2 Give your answer to…

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Q: 2. Find the average value of the function x2 In(x) for 1 5x<3 Show your work in evaluating any…

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Q: Determine all the relative minimum and maximum values, and saddle points of the function h defined…

A: Here we have to find relative maximum ,mininmum points and saddle points.

Q: Arcsin(x/y) = 4x + 3y

A: To find out the double derivative.

Q: A test has multiple choice questions with 3 choices for each answer; only one answer is correct for…

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Q: Find the slope of the function f(x) = V5x at x = 5. V5/2 -25/2 1/2

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Q: Use the Integral Test to determine whether the series is convergent or divergent. -2n ne =1 Evaluate…

A: From integral test of a series we get,   If a function f(x) is continuous , positive and decreasing…

Q: de

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Q: Use the Integral Test to determine whether the series is convergent or divergent. (If the quantity…

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Q: Find the area between the curves f(x) and g(x) 2. f(x) = 3x, g(x) = x² – 3x + 8

A: We will find the area between the two curves.

Q: Question 1 ( (a) Use the Second Derivative Test to find the local extreme values of the function…

A: As per guidelines, I can answer only one question. Since you have asked for multiple, so I did first…

Q: Problem #2: Differentiate f(x) = [(6x³ – 3)(7x² + 8x – 1)]° and solve f'(2). %3D Solution: Reason:

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Q: From Rogawski ET 2e section 10.7, exercise 58. Find the first four non-zero terms of the Maclaurin…

A: Given problem:-

Q: A population of bacteria is growing according to the equation P(t) = 2000e0.05t. Estimate when the…

A: Given query is to find the Indicated time.

Q: For the differential equation (x -4)y" + (x- 2)y'+ 2y 0, the singular points are: O None of them x-3…

A:

Q: 6. Figure out the following limits without applying L'Hopital Rule. sin(r- 4) V2r -1-1 b. lim (2²…

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Q: * the Area that lies inside r=3+2 sin 0 out side r=2 is

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Q: Test the series for convergence or divergence using the Alternating Series Test. ∞ (−1)n 7n + 1   n…

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Q: Answer part b

A: Topic:- trigonometry ratios

Q: Solve the system by the method of substitution. (If there is no solution, enter NO SOLUTION.) ** =…

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Q: 1. For the curve x²y? = 25 at (-1,-5), find the equation of the normal line. %3D

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Q: 1. f(г) — 2? + Зх — 6, д(х) %3 2

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

Q: If log, (5x + 6) = 5, then x = You may enter the exact value or round to 4 decimal places. > Next…

A: We will solve for x.

Q: 1. Use the graph of f(x) below to a Determine tht demain and ramge-ofthe fencion D Tind all x such…

A: From the given graph we have to find its required information.

Q: test the convergence ad diivergene

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Q: If h(x) = V6 + 5f(x), where f(2) = 6 and f '(2) = 3, find h'(2). %3D h'(2) = %3D

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Q: Question 11 Find the area of the triangle having the given measurements. Round to the nearest square…

A: Given    Angle C = 100°   Side a = 3 yards    Side b = 8 yards

Q: Mathematics

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Q: 3) i.- Given the IVP: y" +3y-4y = 20, y(0) = 0, y (0) = -5. %3D %3D | A) Use the Laplace transform…

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Q: Find the point on the line y = 4x + 3 that is closest to the origin. %3D (x, y) = %3D -

A: Given query is to find the Indicated point .

Q: Which of the following is the particular solution of the differential equation dy = e ;y = 1, when x…

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Q: Which of the following statements is true about the function f whose derivative is f'(x) = (x -…

A: Given that f'(x)=x-12x+2

Q: Q2: Determine the type of the two lines (parallel, perpendicular, intersecting, north) and give the…

A: here figure 1  is pependicular line because given that both intersect at 90 degree    in figure 2 is…