2 2 -x+2x- 2, x>0

Q: A function f is said to have a removable discontinuity at a if: is either not defined or not continu...

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Q: 17. Find the area enclosed by the x-axis and the curve y = -x² +9 32 s.u. а. 3 b. 18 s.u. с. 36 s.u....

A: Find the area enclosed by the x-axis and the curve y= -x2+9 

Q: Evaluate f*27 dx. x+3 A.) + 9x + C B.) 3 3x2 + 9x + C 3x2 C.) 9x + C 2 3x2 D.) ++9x + C I + +

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Q: Find all the local maxima, local minima, and saddle points of the given function. f(x,y) = 2x2 +3xy ...

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Q: Q4 (a) By using properties of Laplace Transform, find (i) The Laplace Transform of f(t) = 2e sin 4t,...

A: Let's find. 

Q: A. Evaluate the following integrals by substitution. 1. Sx(2x? + 3)®dx

A: Put (2x2+3)= t  Differentiating both sides  4x dx= dt    

Q: Find the value of k so that the value of f,"(2y – 1) dy is 10. 1 2 4 A) в B) c A D) D 3.

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Q: dy x²+3 dx х-ху 1. Both 2 and 3 2. Integrating Factor – First order Leaner 3. Separable method 4. Ex...

A: Solve  dy/dx= (x2+3)/(x-xy) 

Q: CALCULUS A. How do you define Differentiation? B. Explain the principle of derivative with a given f...

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Q: Find fy (x,y,z), fy(x,y,z), f_(x,y,z), and fyx(x,y,z) for the following. f(x,y,z) = 3x* + 3xy - 5z

A: We need to find derivative of given function.

Q: What is an antiderivative of **+2, x2+1 .. x + arctan x-5 2x +3 x + arccot x x + 2arctan x +1 A. D.

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Q: Evaluate the integral fw(2w + 3)² dw A.) w+4w3+w2 + C B.) w+2w3+9w2 + C C.) w2(w2+4w+9/2) + C D.) 2w...

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Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for th...

A: Given problem

Q: The definite integral (-+) dx when evaluated is equal to - 11 Find the value of a." 12 3Vx. a

A: Given ∫49-xa+13xdx = -1112we know that∫xn dx = xn+1n+1 + C

Q: Using the fact that the centroid of a triangle lies at the intersection of the triangle's medians, w...

A: We can find the centroid as below using the required formula.

Q: Solving by variation of parameters 4y" 4y'- 8y 8e-*, we find that: O u_1=(-2/9) e^(-3x)and u_2=-(2/3...

A: Auxiliary equation and variations parameters

Q: M(x,y) dx + (xe*y – 4xy + 2) dy = 0

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Q: questions

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Q: pany manufacturing calculators, the cost, revenue, and profit equations are given by C = 90,000 + 30...

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Q: Calculate the first-order differential equation below using transformation y = xv. dy x+3y= 2x–y dx

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Q: Question 15 Determine the equation of the curve whose tangent line at any point (x.y) is e* – sin x ...

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Q: P(#) Question 4: When working with rational functions of the form f (x) = and the function does inde...

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Q: (2a+1) (x+2) (x–1)

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Q: Given an ordinary differential equation in the form: (xy + y² + y)dx – (x + 2y)dy = 0 (Eq. Test the ...

A: According to question,Given Differential equation,xy + y2 + y dx - x + 2y dy = 0

Q: Question 4 of 10 2 -10-8 -6 -4 -2 2. 4. 6. 10 -6 -10 y 10 4 -10 -8 -6 -4 -2 2 4 6 8 10 -6 -8 10 y 1...

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Q: Sketch a possible graph of a function that satisfies the given conditions. f(-1) = -7; lim f(x) = -2...

A: Given that f(-1) = -7. Therefore (-1,7) is a point on the graph .when x tends to -1 from the left si...

Q: The rate of change in the profit (P) with respect to the number of units sold (x) is 0.0006x² + 10. ...

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Q: For the Ordinary DE y '= f (x, y) to be guaranteed to have a unique solution containing the point (x...

A: Here we have to find when the ordinary differential equation y'=f(x,y) to be guaranteed to have a un...

Q: Find the area enclosed by the x-axis and the curve y = -x² + 9.

A: Given, We have to find the area enclosed by the x-axis and the curve y=-x2+9.  

Q: Solve the given differential equations FODE.  Solve each and show complete solution.    (3x – y – ...

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Q: (sin x 1) dx + (cos x+ 1) dx = C.)-1 D.) - (1+) A.) -89 В.) -91 A B в) А

A: Given:       ∫-π40sinx-1dx+∫0-π4cosx+1dx Apply sum rule:         ∫fx±gxdx=∫fxdx+∫gxdx      =∫-π40sin...

Q: Consider the graph of f. y 4 3 1 1 2 2 3 4 5 6 7 8 9

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Q: (3メーy-4) dy (x+y-4)dx when x« 3, y=7

A: As per our guidelines we are supposed to answer only one. Kindly repost others question as a separat...

Q: Explain what it means to say that: lim, h(x) - o and lim h(x) x →5+ – 0.7. x →4 As x approaches 5 th...

A: According to question,Given limits,limx→4 hx = -∞,andlimx→5+ hx = -0.7,

Q: f(x) C B. A D (a) At which of the labeled points isf' (x) positive? Negative? Zero? f'(x) is v at A....

A: f'(x) at any point means slope of the tangent line drawn at that point. If  tangent line makes an an...

Q: Given f(x, y) = 9xy® – 6x*y. Compute: a?f ду? ||

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Q: Š F(x)dx = 5, f(x)dx = 2, and f(x) dx = -1, find ſ f(x)dx. If %3D а. — 2 b. 2 с. -3 d. 3

A: Topic:- integration

Q: the coefficient of the fourth term in  the expansion of  (0.5 – x)10 a. 15/19 b. 17/16 c. -15/16 ...

A: We will find the fourth term and then it's coefficient. 

Q: 5. If f cb 5dx + 4 V8x? . = 2, what is the value of b? a.) 2 b.) 4 c.) 8 d.) 9

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Q: Use the chain rule to find D (f o g) (–1,2) for f(u, v, w) = (v² + w², u³ – vw, u²v+ w) and g(x, y) ...

A: This question is related to derivative of composite function.

Q: Calculating the necessary aircraft heading to counter a wind velocity and proceed along a desired be...

A: Solution: Let the angle between the plane speed and wind speed be beta and the ground speed vector b...

Q: A penny of 0.75 inches in diameter is randomly dropped 100 times on a customized Go board. It inters...

A: Diameter of penny = 0.75 inches Probability of intersect of lines = 70100 probability on not interse...

Q: (3 cos³ x-1 7. To evaluate dx, the integrand can be transformed to? 1-sin? x a. [(3cos³x+ csc²x)dx b...

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Q: Find the Interior angles of the triangle whose vertices are (-1, -3, -4), (4, -2, -7) and (2, 3, -8)...

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Q: 5dx 5. If f 4 8 +1 = 2-, what is the value of b? a.) 2 b.) 4 c.) 8 d.) 9

A: We have to find the value of b

Q: Suppose f is a quadratic function that has roots x = – 3 and x = 6, and f(0) = 15. We will w a funct...

A: Given: Root x=-3  and x=6 f(0)=15

Q: K石Xuts

A: ∫ Sin-1 x dx   ....(1) Using integration by parts ∫ f1(x)*f2(x) dx = f1(x)∫f2(x)dx-∫[d/dx(f1(x)*∫f2(...

Q: Solve the given linear differential equation with constant coefficients. Solve each and show complet...

A: Its A.E. is D4 – 4D3 + 7D2 – 4D + 6=0                            (D2+1)(D2-4D+6)=0 Now, D2+1=0      ...

Q: Question 16 dx What should be the rewrite of the integrand of S so that the resulting integral is in...

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Q: B In Problems 17-34, use implicit differentiation to find y' and evaluate y' at the indicated point....

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