Evaluate the difference quotient fla +h) – fla) for the function Ar)= 4х-3 (h - 6)/9h 1/9 4/9

Q: xArctanx - Invx² + 1 = y

A: Topic:- derivatives

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Q: The solution of the ordinary differential equation -y(4) + 4y" = 0 is: O c_0+c_1 x+c_2 e^(3x)+c_3…

A: Given -y(4)+4y''=0To find solution of Ordinary Differential equation:

Q: - Find the point of tangency and the equation of the tangent line passing through the point p(-4,-2)…

A: Given: Now, f'(x)=-3-2x. At (-4, -2), slope = -3-2(-4) = 5. So, the equation of the tangent line is…

Q: 3) Evaluate the Riemann sum for f (x) = x² – 2x, a = 0, b = 3,n = 6. Taking the sample point to the…

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

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Q: dy_x² +2x(1+x*) tan" x (1+x*) dx O Op tion 1

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Q: For the following function f(x), find f(0) and f(2). if xs0 x2 f(x) = if 0 <x<2 x+3 if 2sxs4 4-x…

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Q: 1. Find two sets of polar coordinates for (x, y) = (-V3,1, one with r> 0 and one with r< 0, both…

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Q: Draw a right triangle containing 0, so that the opposite side is 2, the adjacent side is 5, and the…

A: Topic:- trigonometry ratios  Note :- as per our guideline if more than one question uploaded than…

Q: The technique used to prove that dk =- 3x + 3V3 tan" + C %3D x2 + 3 3 is O Integration by Parts O…

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Q: Graph the function. Use the graph to find the indicated limit, if it exists. x20 lim f(x), fx) = -…

A: solution:-f(x)=x3 ,         x≥0-6x  ,    x&lt;0left hand limitlimx→0-f(x)=limx→0--6x=0right hand…

Q: O O O O For the differential equation (x2-4)y" + (x-2)y'+ 2y 0, a regular singular point is: O x-4…

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Q: Using appropriate substitution, S [sec³ (2x) – 2] tan(2x) dx is equal to

A: integration

Q: For the differential equation (x² – 4)y" + (x – 2)y' + 2y= 0, the singular points are: %3| x=2 and…

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Q: Use the graph of y fx) shown at right to find the domain of f. 345) (-63) 9,3) The domain of fisO…

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Q: Given y, (x) = x? is solution for the differential equation x²y"-3xy' +4y= 0 Using the reduction of…

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Q: Evaluate the following integrals. 4x545 2. 3. fx Vr? - 4dx 4. S(2- sin 4r) dr

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly re-post other…

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

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Q: cos(xy) + secy = 5

A: To find out the second derivative y".

Q: 24. Find the volume formed by rotating about the y -axis the region enclosed by: x = 9y and y3 = x…

A: Here, the curves are x=y3 &amp; x=9y. Now, the points of intersections are at: y3=9y⇒y=0,3   because…

Q: Evaluate 3x- 2y ds where C is the line segment from (3,6)to(1,-1)ts -58.240 58.240 O -57.991 O Non…

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Q: How do i solve the attached taylor series question?

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Q: Using the method of undetermined coefficients, a particular solution of the differential equation y"…

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

Q: 1 Evaluate the limits 1im - x+2 X* 1/4 1/2

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Q: Graph the function. Use the graph to find the indicated limit, if it exists. x3 x20 lim f(x), f(x) =…

A: Let's find.

Q: 1 Evaluate. 5P3 • 6C4 900 300 150

A: Use the formula and evaluate.

Q: Decide whether the given relation defines a function, and give the domain and range. Year (x) 2005…

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Q: The technique used to prove that x4 x3 , dx =- 2x + 2vZtan- ( 2/2tan + C x2 + 2 3 is Long…

A: We have to find the method

Q: Ssec10dE

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Q: If ex) dx = 33 and/ ocx) dx = 16, find (4f(x) + 59(x)] dx.

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Q: Mathematics

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Q: Consider the differential equation (x- 1)y" + y' = 0. By using power series so- lution about the…

A: Please see the below picture for detailed solution.

Q: Q3: Find gradient of the following function at given point 1) f(x, y) = y –x, (2,1) 2) g(x, y) = y –…

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

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Q: Using decomposition into partial fractions, 4x2 + 2 J x(x² + 2) is equal to

A: We can solve this as follows:

Q: Solve the second derivative(y") of the following function and simplify the final results. Show your…

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Q: 8. Sketch a graph (different for each) that satisfies the given conditions: a) f'(x) 0 if x -2 (x…

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Q: Determine the values of a, b, and c for Ax) = ax + bx+c so that f") = 6x- 3 and A2) = -1.

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Q: The integral (2

A: Given: ∫124xx2-43dx

Q: 3x+1 5) lim x+ 2x +5 2+Vx lim ²-3x 6) 7) lim 2-Vx

A: Limits

Q: Find and classify all the critical points of f (x,y) = 7x – 8y + 2xy – x² + y³.

A: For critical points put partial derivate=0

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A: This problem gives us the system of linear simultaneous equations. This system can be represented by…

Q: Using the method of undetermined coefficients, a particular solution of the differential equation…

A: Given differential equation is y''-16y=2e4x. The characteristic equation is m2-16=0⇒m=±4. So, by the…

Q: log x y = dy dx 5+5ln5logx x² In5 dy 5-5ln5log x dx x² In5 Option 4 Op tion 3 dy _ 5-5ln5logx x² In5…

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Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

A: Explanation of the answer is as follows

Q: Find the Area bounded by the given curves. y = 2x + 1 ,  y = 7 - x ,  x = 8

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

A: Let A and B denote the events of guessing the correct option of question 1 and question 2…

Q: In(n+24)158 In(103+12 n)200 The sequence is and its limit is

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