Q1// prove one only: tan²x-1 tan²x+1 = 1-2cos²x

Q: (i) Find the shortest distance from the origin to the line 3x + y = 6 and give the coordinate of the…

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Q: Solve the initial-value problem y"+5y'+6y=0, y(1)=2, y'(1) = 3

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Q: Consider the function below. (If an answer does not exist, enter DNE.) C(x) = x¹/5(x + 6) (a) Find…

A: Let's solve.

Q: Evaluate the iterated integral. 2 *4z [In(x) f Jo xe Y dy dx dz

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Q: A tank initially holds 80 gal of a brine solution containing 1/8 lb of salt per gallon. At t=0,…

A: Let's find amount of salt at t=10minute.

Q: 6. Find the general solution of the PDE. The solution u is a function of x and y. U = x-yz +y³

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Q: A fair coin is flipped 5 times. What is the probability of: a. Getting HTHTH, in that order? b.…

A: According to our guidelines we are supposed to answer only the first three sub parts question if you…

Q: 2. In π 2 π ln - 4 e* cos(ex) dx

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Q: 8. Find the length of the curve r(t) = from t = 1 tot = 5. 9. Find the curvature of the curve r(t)…

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Q: Write an equation for a function that has a graph with the given characteristics. The shape of y=…

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Q: 4) The area under the curve defined by the positive function f (x) on the interval [2, 6] is known…

A: We are allow to solve first question only Thank you

Q: Find t for the following terminal points, 0 ≤ t < 2π (a) P(0, 1), = √2 2 (b) P ( - 1/², 1/²³). 1 = t…

A: Let's find t for the given  terminal points.

Q: Below is the graph of y= log₂ x. Translate it to become the graph of y= log₂ (x+2)+4. X -6 -4 -2 2 ?

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Q: Solve 2 cos² (t) - 3 cos(t) + 1 = 0 for all solutions 0 ≤ t < 2π t = Give the exact answers as a…

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Q: Use the root test to determine whether the series converges or diverges. If the test is…

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Q: 00 15. The sum of the series : Ek=0 a. m (-1) ()2k+1 (2k)! b. 픔 C. -2 T 3 d. 5 T

A: First I have arranged the series and then using power series representation of cos(x) evaluate the…

Q: Given that Y₁(t) = e 2¹ and Y₂(t) = e³ make up a fundamental set of solutions to y"+5y'+6y=0, find…

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Q: If ā= 3x - 5y and b = -2x+9ỹ, write the vector 5ã-85 in terms of x and y

A: Given vector are a→=3x→-5y→   and b→=-2x→+9y→. We have to find the vector 5a→-8b→. Now, 5a→=53x→-5y→…

Q: Q3)Evaluate the following integral by using Trigonometric Substitutions Method. dx y = S₂ 9x² +9

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Q: Effect of Luxury Tax on Consumption Government economists of a developing country determined that…

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Q: ) Find (dy/dx) for: tan-¹(x² + y) - eln(x³y) = 5sinh(y)

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Q: 3 tabler W y = JUN 13 MacBook Pro (A)

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Q: . For what values of a are the points (6, 2, 3) and (a, 2, 5) and the line = (2,-1,-2) + t(3,1,-2)…

A: I have appended the formula used in the solution part of the question

Q: 1. The effectiveness of studying for an exam depends on how many hours a student studies. For a…

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Q: Q2// Find the resulting volume of the curve y = sin x cos x rotation about the x-axis if x=0, x=/?

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Q: c. p> 1 7.One of the following sequences is divergent sequences a. 3n² + 2n n5 + 7 n! b.{-1)".…

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Q: Find dy /dx for the following functions: -) y².cotx= [sin(x. y)]-¹ b) y = (lnx+x) tan x

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Q: 27. Check whether the points (0, 7, 10), (-1, 6, 6) and (-4, 9, 6) are the vertices of a ight angled…

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Q: The diagram below is a portion of a graph of a differentiable function f(x). In this graph, which of…

A: Given.

Q: Fibonacci method can be applied if the function is continuous only. O True O False

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Q: Find the volume generated by revolving the given plane area about the given line using the washer…

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Q: The population of a certain inner-city area is estimated to be declining according to the model…

A: Here, the given model is for the population of a certain inner-city area after t number of years:…

Q: Q6) Find the Area bounded by the curves y = √x and x = 2y-y² ,with sketch.

A: First we find the limits of integration.

Q: Use the table of integrals to evaluate the integral. 2 [²³15x³√4x² 15x³ 4x²x4 dx

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Q: Given functions f(x)=√x + 13 and m(x) = interval notation. Domain of f(x) m(x) Domain of f(m(x)) :…

A: To find out the domain of the functions.

Q: Use the Lagrangian method to minimize f(x, y, z) = x² + 2y² + z² s.t. x² + 2y + 3z = 8 Find the…

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Q: The polar equation r(0) = 4 +5 sin(0) is graphed below. 15+ 14 13 12 11 10 8+ 7 6 + 5 O 4+ 3 2 + +…

A: Above question is solved.

Q: If y = ecos(x) then y" + sin(x) y' cos(x)= ***

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Q: 1 1+6402 anges JP

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Q: Evaluate fea cos(2x) dx

A: We have to above integration

Q: The number of bacteria in a culture is given by the function n(t) = 940e 0.1t where t is measured in…

A: To find out the relative growth rate.

Q: Find the derivative of the following function. 3 8x y = In x y'=0

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Q: generated by revolving the given plome area line uning the dirc method. (answers ore in cubic a.)…

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Q: 4. With the fact of 1² +2²+...+ n² = n(n+1)(2n + 1)/6, prove that n n n(n −1) ΣΣ(i-j)² 6 i=1 j=1…

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Q: The value of the following limit Lim (cos(x))ou(x) IS:

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Q: 8. Determine a vector equation for the plane with Cartesian equation: 2x -y + 3z-24 = 0

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Q: Find the exact length of the curve. y = 5 + cosh (2x), 0≤x≤ 7

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Q: Graph the rational function. -5x-15 f(x)= x²+2x-15 Start by drawing the vertical and horizontal…

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Q: 1. Find when y = In (-²). dx Express your answer in a single fraction.

A: The given function,     y=lnx5-2x

Q: By using the differential operator D and it's inverse, solve this equation: y"" - y" - 6y' = ex ex…

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