(x4 - 4x²y²-y4) dx + 4x³ydy = 0; when x = 1, y = 2

Q: Find the general solution to the differential equation dy/dx=x^2/y+3.

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Q: Find the equation of the tangent line to the graph of the function f (x) = sin (7√) at the point…

A: Here we have to find the equation of the tangent line of the function…

Q: "+9y' + 18y = 0

A: Topic:- application of derivatives

Q: = 0 and y 16k (x-3) = 0. Find the area bounded by the parabolas (x - 3)² - 16ky =

A: Given: (x−3)2−16ky=0 and y2−16k(x−3)=0 Graph of the given curves will be as follows

Q: 22. Suppose that lim f(x) = x, what is the value of lim 5. (f(x))² ? x-3 A. 41 C. 45 B. 43 D. 47 23.…

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Q: Evaluate the following integrals. 13 1 sin²x -dx

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Q: Give the general form of the equation of the plane that is perpendicular to the plane x+2y x-4 1-2y…

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Q: 2 x-x² if x ≤ 2 - Let f(x) = 2x - 1 if x > 2 Calculate the following limits. Enter "DNE" if the…

A: Let fx=2-x-x2 if x≤22x-1 if x>2To calculate the following limits. To enter "DNE" if the limit…

Q: T/6 3 coss 3x dx

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Q: $9500   is​ invested, part of it at 11 ​% and part of it at 6 ​%. For a certain​ year, the total…

A: $9500 is​ invested, part of it at 11% and part of it at 6% For a certain​ year, the total yield…

Q: 43. Evaluate: S(2ex - 4x) dx A. 2e*4* + C B. -2ex + 4x + C 4x C. 2ex + C In 4 4x D. 2e* + + C In 4…

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Q: 5. Evaluate the following triple integral. ſſſ (.x² + y² ) dx dy dz D D={(x,y):x² + y² ≤9.15:53)

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Q: Arc length: Find the length of the space curve with vector equation r(t) =(4, 3cost, 3 sint ) over […

A: We have to find the arc length.   According to our guidelines we can do only one question so please…

Q: The gradient of the tangent to the curve y=-3x³ + 4ax² - 5x + 4 at x = 1 is 2. The value of a is 2.…

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Q: . Determine the value of x when the slope is its maximum for the function f(x) = 2cos (3x)

A: Here we have to use the concept of derivatives.

Q: Find the tangent plane (Xo, Yo, Zo) from f (x, y) = x² - 3y²; (0,1, -3)

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Q: Find the slope of the tangent line to the graphof the polar equation 1 r = at Ø= 1-sinø 6

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Q: 4. Determine the Cartesian equation of the line that... a) is perpendicular to x=2+t, y=-3 + 2t and…

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Q: Identify the surface area formed by revolving the graph of about the x-axis y = cosh x, 0 ≤ x ≤ 1

A: Graph of the function÷

Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² +…

A: We first graph x2+y2-6y=0 and y=6-x using a graphing calculator.  The shaded region will rotate…

Q: 6. f(In x)² dx

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Q: the particular solution

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Q: Evaluate the y' and Simplify the answers I Direct trigo functions y = x² sinx + 2xcosx - 2sinx

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Q: u = xz siny + yz cosx + xy tanz

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Q: b. Identify the function's local and absolute extreme values, if any, saying where they occur. -15…

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Q: Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a…

A: Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a…

Q: The volume of a cube is increasing at the rate of 4cm³/min. How fast is the surface area increasing…

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Q: 2. If the first term of an arithmetic sequence is 3 and the common difference is 4, what is the 23rd…

A: Topic = Sequence

Q: Determine the center-radius Form of the equation of the sphere whose- diameter has endpoints at (2,…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find the area bounded by the curves y-x² = -3,x+y = 3 and y = 0.5x.

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Q: 21. Find lim x-5 A. 2 B. 3 x² - 7x+10 x-5 C. 4 D. 5

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Find the volume generated by revolving the area bounded by x² + 4x + 4y + 8 = 0 and y=-2 about the…

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Q: 10. Given the graph below, what is the value of x of the function H(x) is discontinuous? h(x)== A. 0…

A: Since you have asked multiple questions,  we will solve the first question for you. If you want any…

Q: Find the volume generated by revolving the area bounded by y² - 4y - 4x + 4 = 0 and x = 1 about the…

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Q: Solve ₂(x + 1)(x + 2)²(x²-1)dx with and without the even-odd theorems (show both solutions).

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Q: In the quadratic equation Ax2+BX+C =0, describe the roots when B2-4AC is positive. The roots are…

A: The given quadratic equation is Ax2+Bx+C=0

Q: -1 valuate the following expression without using calculator : tan sin (³²) +cos 35 - 12

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Q: mx 13 if x < - 9 - Let f(x) = x² + 3x − 4 if x ≥ −9 If f(x) is a function which is continuous…

A: The objective of the question is determine the value of "m".

Q: Solve ²₂(x + 1)(x + 2)²(x² − 1)dx with and without the even-odd theorems (show both solutions).

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Q: i can't understand your solution

A: We have to explain the solution.

Q: 5. Determine vector and parametric equations of the plane that... a) has the scalar equation 2x-y+…

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Q: Using Pappus Theorem, find the volume formed by revolving about the x-axis the area bounded in the…

A: We have to find the volume.

Q: Find the area bounded by the curves x² + y = 6, y = x, y = -2 and x = -2.

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Q: Consider the point P (-3,-1,5), the line : x = 3 t. y, y = -6t -3₁ z = 2t +1, and the Flane 1² : 7…

A: Given

Q: State the initial value theorem. Verify the theorem for the functions: (a) 3-4 sin t (b) (t-4)² and…

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Q: Determine wether the sequence converges, or diverges. If it Converges, S(2n-1)! 2(2n+1)!S

A: We have to find sequence converge or diverge..

Q: For which of the following integrals should substitution be used, instead of Integration by Parts?…

A: Solution :option D substituition be…

Q: _42. Evaluate: √(√√x - 2)dx 3 A. ++ C x 3 B. - + C x C. 3 +=+ C 2 D. -*²_³+C 2 x 12 Evaluato: ((2x…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Evaluate the y' and Simplify the answers Inverse trigo functions y = √x² - 4+2arc(csc)

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Q: a. Use the definition mtan = lim f(a+h)-f(a) h h→0 b. Determine an equation of the tangent line at…

A: As we know that; The slope of the tangent line to the curve is equal to the derivative of the…