Q1. Let r(t) = i + 3tj + t²k be the position of a particle in space at time t. Find the following: 1) The particle's velocity v(t) 2) The particle's acceleration a(t) 3) The time t at which the particle's speed is 5.

Q: Consider the following. 0.75 +² dx V9-16x² 3 Let x = sin(0) and determine the following. 4 dx = de x…

A: Given I=∫00.75x29-16x2dxI=∫00.75x232-(4x)2dxLet  x=34sin(∅)Differentiate dx=34cos(∅)d∅As x=0 →∅=0…

Q: 3a. Find the coordinates of the relative maximum and relative minimum of the following equation:…

A: solution:-f(x)=x-32e2xf'(x)=x-32ddxe2x+e2xddxx-32…

Q: A projectile is fired in the air from a height of 125 feet. Its velocity (in feet per second) t…

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Q: 2) If a + b + c = 0, show that a × b = b × c = cxā

A: Solve the following

Q: Given that f(-5)=2, f'(-5) = -4, g(-5) = -7, g(-5) = 6,

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Q: * Use the graph below to answer questions 7 and 8* The equation of the graph shown below is written…

A: This question can be solved using the concept of horizontal and vertical asymptote.

Q: Consider the level surface defined by the equation x² - y² + z² - 4xyz = 6, find the following: a)…

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Q: 6. y у = хбезвах y = sice те 2x Lex

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Q: 8 1 1 -dx אן

A: If the integral gives finite value , it means integral converges otherwise diverges.

Q: ylor Polynomials: -- Find the 3rd order Taylor Polynomial for f(x) x centered at a = 2.

A:

Q: Q1: Answer 2 branches only A. Find the general solution of the following Initial Value Problem…

A: Given :y''-2y'-3y=5cos2t

Q: B- for the function below, the domain and the range is respectively -2+√1-x (-∞0,00) & [-2,00)…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Verify that the indicated function y g(x) is an explicit solution of the given first-order…

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Q: dx 3 Losx

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Q: dy x3 dx 2+y²

A: Let's solve given diffrential equation.

Q: Q.1) Choose the correct answer for the following: (choose 5 only) 1- The vector from point P=(2,2,1)…

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

Q: 4x² +5=3x

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Q: find fxe*dx

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Q: A person starts walking from home and walks: 2 miles East 5 miles Southeast 6 miles South 6 miles…

A: Use vector concept

Q: D-the result of the following limit is 1² lim x-0 In (sec x)

A: Let's evaluate given limit.

Q: a. Show that f has a removable discontinuity at x = 3. f(x) = x²7x+12 x + 2 x = 3 b. Redefine f(3)…

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Q: Evaluate the following integral − (x - 1)(x-2)(x − 3) -

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Q: f cos² x dx

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Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

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

Q: I 2ex e3x tex dx

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Q: Calculate the derivative of the function below using the quotient rule. y = 2-10 √x + 5x8 f(x) = and…

A: Use quotient rules

Q: give the integral of volume of a solid of revolution when the region bounded by y=x2, y=-2x-1, y=0…

A: This is a problem related to volume generated by solid revolution. Based on the general formula and…

Q: Let f(x) = 3 sin(x) + 2 cos(x). Find the following: 1. f'(x)= 3 cos(x) - 2 sin(x) 2. f'(5)-|

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Q: C-the derivative is y=0³ e 28 cos 50 e 20 (3cos 50-20 cos 50-50 sin20) it's 02e-20 (3cos 50-20 cos…

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Q: Q5) Solve the following using Trapezoidal rule with n=6 2 f(x) = [²xtnx. dx 0

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Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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Q: The equation of the graph shown below is written in the form y=- x-h D A 7. The value of t is i than…

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Q: which means that and thus 2x 5x + 3 and g(x)= and g'(x) = D II 5x + 3

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Q: 7. Prove that: (3) (a) (4) (b) sin20 cos20-1 in (-0) + cos (- 0) = cost -cote =

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Q: ) R.J&M Company manufactures furniture such as sofas and tables. In their current inventory, a total…

A: We have to find the number of sofas and tables.

Q: State the intervals of increasing and decreasing behavior in the function f(x)=x^3+2x^2-4x+5.

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Q: 3- The result of dot product between A=(2, 3, 1) and B=(-1, 5, 1) is: a) A. B=14 b) A. B=-34 c)…

A: 3.

Q: Recor Numerical Response # inverse of this function box. Record the value

A: Range of original function is the domain of its inverse function.   Given function

Q: Determine the point(s) (if any) at which the graph of the function has a horizontal tangent line.…

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Q: B- The derivative is y = ln (sec (In 0))

A: Solution ) y = ln (sec(ln θ)) Using chain rule  dy/dθ = (ln m/dm) × (dm/dn ) × (dn/dθ ) m = sec(ln θ…

Q: Jason acquired a $10,000.00, 91-day, Province of Alberta T-bill on its date of issue for a price of…

A: Given problem:- Jason acquired a $10,000.00, 91-day, Province of Alberta T-bill on its date of issue…

Q: The result of dy/dx for the following function is COS X y = 1+sin x

A: In this question we have to find the differentiation.

Q: 4. Find the value(s) of a for which and are orthogonal: a) (2,-4,5) and (a +1,3,-a +3) b) -…

A: As per guidelines we must answer only one of multiple questions given. Please resubmit the remaining…

Q: Q5) Solve the following using Trapezoidal rule with n6 f(x) = f*xinx. dx

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Q: Calculate the derivative of the function below using the quotient rule. y = 210 √x + 5x8 f(x) = and…

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Q: How long did it take for an investment of $21,250 to grow to at least $24,000 at 2.50% compounded…

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Q: 5. Use the Squeeze Theorem to evaluate lim sinz 1-00

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: 2- The order of equation 4y"" + 2(y")5-5xy = 0 is.

A: Note: As per bartleby guidelines, I can answer only one question. So, kindly repost the other…

Q: The region enclosed by the graph of y = ex², the x-axis, and the lines x=0 and x=2, is revolved…

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Q: 7. S. 5x4x² 3 sin 2x y = 2 y = 4

A: Solution ) y = 25x .34x^2 Take log both side  log y = log ( 25x .34x^2 )  [ log m.n = log m + log n…