For which value of a is the differential equation (y² + axy³ )dx + (Ky²x² + 2xy) dy = 0 exact

Q: √√1-25x² dx

A: This question can be solved by the concept of some special integrals.

Q: ered # tion Bi Q) choose one only 1. If (x + y)² = x² + y² prove that = - dx 2. If y = sin³ () cos³…

A: To find the differentiation of given functions.

Q: Find the equation of tangent line to Graph of f(x)=3 x In(5x-4) at point where x=.1

A: Solution:

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A: Given

Q: It is known that for a function f(x), f'(1) = 0 and f" (1) = -0.5. What does the Second Derivative…

A: This question can be solved using the concept of second derivative test.

Q: The graph of a function y = f(x) on the interval [ - 3, oo) is shown below. Use the graph to answer…

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Q: 1 x² + y² = 4

A: Given: 1x2+y2=4

Q: You are tasked with designing a cylindrical can. The material for the top and bottom of the can…

A: This question can be solved using the concept of maxima and minima.

Q: Given the function y = x(x + 1)3. Determine the value of its second derivative at x = 1.

A: Given the function  y=xx+13. We have to find the value of its second derivative at x=1.

Q: The position of an object moving along a line is given by the function s(t)= - 16t+80t. Find the…

A: The objective of the question is determine the average velocity in the given intervals.

Q: The integral of sin x³ dx is cos x + Option 1 cos³ x 3 + C cos x + Option 2 cos² x 2 + C

A: Given ∫(sinx)3dx=∫sin3xdx

Q: 1) If y = (x − a)√2ax - x² + a² sin−¹(*—ª),t ), then y'= 2√2ax-x² a is constant.

A: As per instructions, Here is the answer of question 1

Q: 3. I. Evaluate each determinant. -1 5 3 2 3

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Q: TRUE or FALSE: 1. The integer 5047 is a prime numbe

A: To write down that the given number is a primer number or not.

Q: 1) If y = (x − a)√/2ax - x² + a² sin a is constant. sin-¹(*), then y' = 2√/2ax - x² a

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

Q: Find lim f(x) given the graph of f(x) shown above. (If the limit does not exist, enter Ø.) x-1+…

A: We have to find value of given Limit.

Q: 3. Use the cross product properties to prove the relation (a - b) × (â+b) = 2(â × b) given a = (1,…

A: Given,a=i-3j+2kb=-2i+0j+k

Q: Solve the equation: y" - y" -2y' = 0 Oy=c₁e* + c₂ + c3e²x y = ¢₁e²^³ + c₂e³ + c3e²x O

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Q: If the definite integral of (1 + sin y)dy with lower limit equal to zero is π+2, its upper limit is…

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Q: onvert the point p = (2,7) in the polar coordinate system to its artesian coordinate equivalent, and…

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Q: Q3 Calculate the value of the following integeral: dx (1) S 2x√x-1 etan ¹x 1 + x² - dx

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Q: 1. For each of the following solve the system that is given. a) : (x, y, z]-[5,-1,3]+[4,-5,2] and…

A: Concept: The system of equations in complex form:…

Q: 4. x² + y² = 25 at point (3,4) 2

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Q: 1. If F(x) = - eta dt, find F(1) and F'(x).

A: If Fx=∫exe et2 dt, then to find F1 and F'x.

Q: e the differential equation e2x dy +2e²x y = 2x

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Q: * Let R be the region in the first quadrant bounded by x^2 +y^2 = 4, y^2 = -x+4 and y=0. Set up the…

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Q: 6. I. Evaluate each determinant. тут 3-3 4 1 -5 0 -1 -4

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Q: Solve for the area bounded by the graphs of y = √√√x + 2, y = x + 2, x = 2, x = 4

A: Graph:

Q: Determine the interval(s) where f(x)-In (5x+10) is continuous. It is continuous in the interval

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Q: af axdy of f (x, y) = xy(x+y — 1) — x² Find-

A: The given function is: fx,y=xyx+y-1+x2   As we know that; The Power Law: ddxxn=nxn-1 The Product…

Q: я f (x) = (x2 + 3x)³ . (4x3 - 5x) 7 - -

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Q: Using the letters in the word COSINE arranged in random order, what is the probability that the…

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Q: The position of an object at time t is given by the parametric equations x = 3t² + 1t y = 3t² + 3…

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Q: A cylindrical can without a lid is to be constructed to contain 800 ml of liquid. Determine the…

A: To find the dimensions that minimize the amount of metal needed to make the can.

Q: Evaluate the double integral: So Son VV (Hint: Change the order of integration to dy dx.) sin(7³) dr…

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Q: In 7 + 4√3 2.63391 ≈

A: The given expression is  ln7+43

Q: 3. A farmer applies x tons of fertilizer and y tons of pesticide to a crop, the yiled will be f(x,…

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Q: IVICCE dy Find from the following equations dx Problem (iii) x³ + xy = 0

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Q: Analyze and sketch the following curves.Indicate the intercepts, asymptotes, and critical points

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Q: The rate of change of revenue (in dollars per calculator) from the sale of x calculators is R'(x) =…

A: Here, the rate of change of revenue after the sale of x calculator: R'(x)=(x+5)ln(x+5)

Q: lim x4 1 x³-64 Ꮳ 5 1 vx2+9

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Q: The graph of the rational function f(x) is shown below. Using the graph, determine which of the…

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Q: p and q are complex numbers such that pl = 7√2 and p+ql = 12√//3. On what interval must g fall on? O…

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Q: Let R be the region in the first quadrant bounded by x^2 +y^2 =4, y^2 = -x+4 and y=0. Set up the…

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Q: Find the area (in square units) bounded by the parabolas x² + 2y - 8 = 0. a. 7.10 sq. units b. 7.01…

A: Here we have to find the area bounded by the parabola.

Q: West Z dt x North JOAN dx dt ANDRES = 25km/hr dy dt y 18km/hr

A: Given: Speed of Andres  = 18 km/hr Speed of Joan  = 25 km/hr

Q: x = 1. 2. Find the derivative of f(x) = 3x² - 5x at x = 1 using the formula f'(x) = lim f(x)-f(xo)…

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Q: SET-UP a triple integral that will solve for volume of the solid S bounded by the sphere x² + y² +…

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