Find the general solution of the differential equation. (Use C for the constant of Integration.) dy 27 - 9x %3D dx -9x + 9 y =

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A: Given Point P(1,4) & inclination θ=60To find equation of tangent:

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Q: To find two real numbers whose difference i and whose product is minimum, we can find minimum value…

A: Topic:- calculus

Q: al squares fr ame if the pie 16

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Q: I. Find the general solution of the following: dy 2x 1.- dx y dy 2. xy dx 3. dy = (6e3x+ 1)dx

A: We have to find the general solution.     According to our guidelines we can do only one question so…

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Q: f'(x) =-+e²* +x²and f(1)=. Find f(x) Given

A: Here, given that: f'(x)=1x+e2x+x3⇒f(x)=∫1x+e2x+x3dx+C⇒f(x)=∫1xdx+∫e2xdx+∫x3dx+C⇒f(x)=ln…

Q: Use the graph to find the following limits. a. lim f(x) b. lim f(x) x -1 X-1 a. Find lim f(x) or…

A: This question is related to limits, we will solve it using given information.

Q: 1. A line passes through the points A(2, 3) and B(-2, 1). Find a vector equation of the line. [x, y]…

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Q: For f(x) = 2x - 8x° +3 find the following. %3D (A) f'(x) (B) The slope of the graph of f at x = 1…

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Q: Find each limit. Use - o or ∞ when appropriate. 4x-4 f(x) = - (x- 4)? (A) lim f(x) (B) lim f(x) (C)…

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Q: Differentiate the function. 2 + g(t) = In t(t? + 1)4 V8t – 1 g'(t) =

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Q: Given the triangle 13 find the length of side x using the Law of Cosines. Round your final answer…

A: This question is related to Triangles, we will solve it using given information.

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Q: Use algebra and the properties of limits as needed to find the given limit. If the limit does not…

A: We can find the limit of the function. Firstly make factor in numerator and denominator and solve .…

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Q: Use the graph of the function f shown to the right to estimate the indicated function values and…

A: topic- limits

Q: Find all the derivatives of the following functions f (x) = x° + 4.x² + 3x³ – x² + 6 5 1. 1 g(x) :…

A: 1) f(x)=x5+4x4+3x3-x2+6Differentiate…

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Q: 3

A: We will find the limit.

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A: Given

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A: P(x) has roots of multiplicity 2 at x=1 so (x-1)2 is a factor of P(x).  P(x) has roots of…

Q: Write the function below in the form y = f(u) and u = g(x). Then find as a function of x. %3D y = V…

A: Given:        y  = 3x2-4x+2

Q: 6. Vector, scalar or meaningless? Explain. ») (ä - 5) + (7 - E) b) (å x 5) – (¿ x đ) c) dlã x )

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Q: f'(x)=-+e2* +x² and S(1) =. Find f(x) Given %3D

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Q: Use the graph to find the following limits and function value for each value of a. i) lim f(x) i)…

A: Given query is to find indicated limits.

Q: Determine the antiderivatives of the following functions: 1. V36-x² dx 2. J 9x2+36dx 1 S- x In…

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Q: To find the distance across a river, a surveyor choose points A and B, which are 224 m apart on one…

A: In this question we have to find AC and distence across the river.

Q: Q2. Do as required 3. Evaluate: lim (-) X0 sinx

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Q: Write a in the form a = a-T+anN at the given value of t without finding T and N. r(t) = (- 2t + 3)i…

A: The Solution is given below

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A: sum of number is 23 let a number = x  other number is 23 - x

Q: A tire swing attached to a tree branch swings with an arc length of 40 feet on its first swing. On…

A: Question- A tire swing attached to a tree branch swings with an arc length of 40 feet on its first…

Q: Problem 12 Find the following indefinite integrals (a) S(9x² + 8x +3)dr (b) S(x-4 – 9/I)dr (c)…

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Q: G В R K + Match each equation with a graph above E 4(1.49)" a. blue (B) |- v |2(1.22)* b. orange (0)…

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Q: 2) Use the Chain Rule to express the second derivative of f •g in terms of the first and second…

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Q: pints A and B are separated by a lake. To find the distance between them, a surveyor locates a point…

A: Given query is to find the distance AB.

Q: Find the velocity and acceleration vectors in terms of u, and ue en r=6 sin t and 0= 9t

A: The velocity is given by            v = r' ur +rθ' uθandThe accerleration is given by        a =r"-r…

Q: Find each function value and limit. Use -∞ or co where appropriate. 7x* - 14x2 f(x) = 8x° +4 (A) f(-…

A: topic- functions and limits

Q: To find two real numbers whose sum is 46 and whose product is maximum, we should find the maximum…

A: It is a true and false type question. Answer  is false

Q: Q1) Use the Laplace Transform To Solve the Given Initial Value Problem: y +3 y + 2y = 4e' y (0) = 1,…

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Q: 2. The number, N, of bacteria in a culture at time t, in hours, is N(t) = 1000[30 + e a. What is the…

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Q: Evaluate the limit In(x) lim x+1 x2 - 19x+ 18 a. 1 19 O b. 19 C. 1 17 O d. None of these. е. —17

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