Given the function graphed below, evaluate the definite integrals. 4+ 3 2 1 -1 7 -1 -2 -3 -4 1 S.³ f(x) dx = [ ľ 1 f(x) dx = [ 2 3 5 6 7

Q: Suppose that the position of a particle is given by s(t) = 5t³ + 6t+9. (a) Find the velocity at time…

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Q: Consider y=√√x+1. (a) Find its inverse relation. Is this relation a function? Why? If the inverse is…

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Q: Evaluate ſ F . n dS if F = (x + y² ™)ī − (2x)j + (2yz)k and $ is the surface of the plane 2x + y +…

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Q: Answer the following True or False: If f(x) is a differentiable function such that f'(-4) = 0, then…

A: Given that the function f(x) is differentiable function and f'-4=0 We need to verify whether its…

Q: Given the curve shown below, determine if the slope of the curve at x = negative, or zero. 4 3 2 O…

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Q: The opposite vector of 10 N [S80°W] is 10 N [W10°S]. True False

A: Please see the below picture for detailed solution.

Q: For the following equation, find Answer: dy da || y = -4x5 8x³ + x² +9x

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Q: 1,-1, 3), 6 = 2-(0, 5, -2) Find 52 +22-46 C a Let a = O (5, 1, 1) *(5, 7, -1) O(18, 35, 12) O(-14,…

A: Topic:- application of algebra

Q: 8. Determine the dot product of u = [5,-3,1] and v=| 1v=[2,-2,3].

A: Please see the below answer.

Q: functions f (x) = 2 and g(x) = 1 (i) Consider the (a) Write down the domains of the functions f (x)…

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Q: Σa_₁ (-_^_-) n² 'n n+1 Select one: O True O False is convergent.

A: To determine whether the following statement is True or False.∑n=1∞ nn+1n2 is convergent.

Q: Find the value of C so that y(t) = Ce2t satisfies the initial condition y(1)=1

A: Substitute t=1

Q: -6-5-4-3-2-1 6 I 4 3 2 L -2 -4 -5 T 2 3 4 5 6 X

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Q: If {an} and {bn} are divergent, then {an bn} is divergent. Select one: O True O False

A: The objective of the question is determine the choosing the correct option.

Q: Two cars are moving towards an intersection. One car is 170 meters north of the intersection and…

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Q: Which if the following is a power series representation of the function f(x) a. Σ(-x - xn+¹) n=0 Ob.…

A: We have to find the power series representation for given function.

Q: What is the indefinite integral (anti-derivative) { cos(x) dx? ○ sin(x) + C cos(x) + C - sin(x) + C…

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Q: Consider the points A(3, — 5, 1), B(7, — 1, 0) and C(-1, 3, 4). Find 2AB + BC. O(-1, 2, 3) O(0, -10,…

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Q: Verify that the following function is a probability mass function, and determine the requested…

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Q: 4) Activity 5: Check for Understanding (10 mins) NOV ob For the equation of y²dy = x(xdy - ydx)e*/y.…

A: We can find the degree of the given function and differential equations.

Q: Use the graph of ƒ (x) = x² below to find a number & such that x² − 1| < 0.5 whenever 0 < |ï − 1| <…

A: The graph of the function fx=x2 is given To find the value of δ such that x2-1&lt;0.5 whenever…

Q: Find the values of x, y and z that correspond to the critical point of the function 2 = f(x, y) =…

A: The given function fx,y=4x2+8x+7y+3y2 To find the critical points of the function

Q: Consider y = √x+1. (a) Find its inverse relation. Is this relation a function? Why? If the inverse…

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Q: 00 3) Use the integral test to determine whether the series k=1 ke-2k diverges converges or

A: We have to check weather the given series is convergent or Divergent in nature.

Q: 2.4 Write functions of the following graphs. 2.4.1 2.4.2 + -3 -2 -3 N 0 -1+ 34 2+ 0 - 2

A: Above question is solved

Q: egrate the following by hand, shc 9 (a) 3 3 √x³ - 24+8) dx

A: We can solve this as follows:

Q: 1. sin x sin 2x + cos x cos 2x = COS X

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Q: y 3 2 1 -1 -2 -3 -4 1 2 3 4 5 6 X

A: We can find the Domain and Range of the function.

Q: help

A: Acute angle are measured from 0 to π/2

Q: interval

A: From the graph, we need to find the values of x for which f(x)  is greater than 5.

Q: Determine the general solution of each of the following equations: (a) y" + 2y' + 5y = 3sin2x

A: a) Given:         y''+2y'+5y=3sin2x         5yx+2ddxyx+d2dx2yx=3sin2x This differential equation has…

Q: d the equation of the tangent line to the curve y = 5x cos x at the point (7, e equation of this…

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Q: y=x5, mn=-1/80

A: Given problem:- Find the equation of the line normal to a given curve y=x5 and having a given slope…

Q: Solve x (az + √2) dx y (az + √2) sin (ay²) dy + (az − √2) dz = 0 4√/2ln |az + √2 = C 4√/2ln|az +…

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Q: f(x) = -2x² + 7 7x 10 - if x ≤ −1 if x > -1

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Q: Use following se k Z K-I the integral test Series to decide converge

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Q: Find f(x) such that • ff(x) dx = 1/√ √ x² + 4 + C

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Q: 3. State the components of a unit vector that is perpendicular to the vector = (5,2,−1).

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Q: 3. xy = a², y = 0, x = a, x = 2a.

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Q: Solve (y³ + 2y² +9y+18) dx = (5x²y² x²y + 17x²) dy

A: integration using partial fraction

Q: Consider the function f(x) = 1-5x², -4≤ x ≤ 1. The absolute maximum value is and this occurs at x =…

A: Consider the function fx=1-5x2, -4≤x≤1.To determine absolute maximum and absolute minimum value of…

Q: The depth (in feet) of water at a dock changes with the rise and fall of tides. The depth is modeled…

A: Given: The depth function: D(t) = 2sinπ4t+5π4+5 Depth is changing at 6 a.m. t = 6

Q: Can this also be solved using the mean value theorem? Thanks!

A: Given.

Q: The function f(x) = 2x³ - 39x² + 216x 3 has two critical numbers. The smaller one is x = and the…

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Q: Determine whether the following relation represents y as a function of x. -6-5-4-3-2-1 y 7r 6 L 5 4…

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Q: 04115

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Q: Calculate r' (t) and T(t), where T'(t) = ( T(t) = { r(t) = (8+t, (9+t), 2+2t). ).

A: Given vector function r(t)=8+t, -9-t, 2+2t

Q: Calculate: fx²e³dx

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Q: Suppose p′(−1)=−2 and q′(−1)=−5.5.  If r(x)=−7p(x)+10q(x), find r′(−1).

A: We have to find the value of r'(-1).

Q: A manufacturer can produce 2700 cell phones when a dollars is spent on labor and y dollars is spent…

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