Find the direction at the origin of the curve, (a²-b¹) y=x (x-— a)¹ — bªx. Ans. 45° with OX. What must be the relation between a and b, so that it may be parallel to OX at the point x=2 a? Ans. 3a²-V.

Q: If x² + xy + y³ = 1, find the value of y'" at the point where x = 1. I 23 X

A: Here we have to do differentiation.

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Q: Suppose that g(x) = (x + 3)² for x ≥ 0. The domain of g¹ is [a, co) for some a. What is the exact…

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Q: (1) Let A and B be two nonparallel vectors. Show that ||Ã + B||² + ||A - B||² = 2||Ã||² + 2||B||².…

A: We can solve it as follows,

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A: To classify the given differential equation

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Q: Based on the graph, the function is discontinuous at — - (List the values from the smallest to the…

A: A function is said to be discontinuous at all those points where there is a break in its graph.

Q: dy 8. Sy sin(e-y) ey

A:

Q: Find e > 0 such that the area of the region enclosed by the parabolas y = x² - c² and y = c² - x² is…

A: given y=x2-c2and y=c2-x2given area is 270

Q: (c) The tangent line is horizontal if y=✔ Using the expression for y' from part (a), we see that…

A: Note:- As per your demand i solve part c for you with details of red underline Given equation:-…

Q: Suppose that f(5) = 2, f '(5) = 4, g(5) = -5, and g'(5) = 6. Find the following values. (a) (fg)'(5)…

A: given  f(5)=2f'(5)=4g(5)=-5g'(5)=6(a) frm product rule(fg)'=fg'+gf'

Q: Find f '(x) and f "(x). x² 1 + 2x f(x) = = f'(x) = f "(x) = X X

A:

Q: Which of the following is an ordinary, linear differential equation of order 2? +k²xt = 0 d²x +k²x =…

A: Find which equation is linear differential equation of order 2.

Q: Set up the integral that gives the area of the given surface. S= 27 4 S2 2T (2√9-y) 1+ 0 The area is…

A: To solve the given integral

Q: Find the equation of the specified line. y(x) = through (1, 9) parallel to x - 9y = 9

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Q: dy Solve + 3y = e*y², y(0) = 6 by making the appropriate substitution. dx

A:

Q: What is A - B for the following vectors? A = (11.7 m, 225°) B = (13.3 m, 347°) Enter your…

A: Topic:- vector algebra

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A: Solution is given below:

Q: |x|-5 lim x−-5x2–25 ||

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Q: © © © © Τα γλυκά και 4.935 17.45 34.912

A: The given graph shows that the polar curve r=2θ+cosθ for 0≤θ≤π. We have to find the area of the…

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Q: answer

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Q: Classify each differential equation as separable, linear, homogeneous, bernoulli equation. Some…

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Q: 7.f(x) = 10x4 - 3x³ + 8x² - 4x - 8 8.f(x) = 4x5 + 3x² + 9x³ − 8x² + 16x - 24

A: Hi this is your answer.

Q: I need to graph f(x)= 2x2+8x divided by x2-x-20. To do this i need to find the following Vertical…

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Q: d the exact location of all the relative and absolute extrema of the function. g(t) = et − t with…

A: Given: g(t)=et−t with domain [−1, 1]

Q: Find the equation of the specified line. y(x) = through (-4, 8) with slope -1

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Q: If 4x − 2x² <f(x) <x² - 2x +3 for - all real numbers except for x=1, then

A: We have to solve given Questions.

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A: Need to find out the dimensions of triangle and square that will product minimum total area.

Q: Assume A = A₁ + A₂ and A, B = 0. If A₂ = kB, show that k = ● (5) (6) Use the formula x = r' (t)…

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Q: Prove: If a|b and b|c, then a|c. Hint: Use the definition of divisibility.

A: Prove: If a|b and b|c, then a|c.

Q: 2a. First, use your calculator to calculate the log of the molecular weight for each ladder band.…

A: Molecular weight given we find the log of molecular weight.

Q: (sin(5x))³ cos(5x) dx

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Q: Find the values of x, y and z that correspond to the critical point of the function f(x, y) = 3x² +…

A: The given function is: fx,y=3x2+4x+6y+4y2 To find the value of x, y, z that correspond to the…

Q: Question 12 Use differentials to approximate the value of 27.25. Round your answer to four decimal…

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Q: Several months ago, John O'Hagan investigated the effect on the popularity of OHaganBooks.com of…

A: Given that , c1=5000 , c2=6000 , v1=2030 , v2=2090 Construct a liner model.

Q: The gradient of f(x, y) = xy at (x, y) = (−2, 1) is

A: To find gradient

Q: Question #6 - Find the following for the function f(x)=20x²-3x³ a) The coordinates for the relative…

A: Domain of  20x3-3x5 :  Solution:  -∞ &lt;x&lt;∞ Interval Notation: -∞ , ∞ Range of 20x3-3x5:…

Q: do O Which of the following expressions gives the total area closed by the pol for above? •710 Jo 10…

A: We have to solve given Questions.

Q: 7. Let R be the region bounded by curves y = x² and y = 2-x². Find the volume V(S) of the solid S…

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Q: Hi! For the question 1 and 3 we are also looking for the discontinuity of the function. I hope you…

A: Given figure:

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Q: The cost C (in dollars) of manufacturing a number of high-quality computer laser printers is C(x) =…

A: The cost C (in dollars) of manufacturing x number of high-quality computer laser  printers is…

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Q: 3) Use the squeeze theorem to show that the following limit equals zero. Show all work TT lim (√x³ +…

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Q: Let f(x) = sin(√x) +3 Find the slope of the tangent line to the curve y = f(x) at the point where x…

A: To find slope of tangent line.

Q: dy Given x -=2y;y (1)=2; Then y (3) = 20. dx True O False

A: