9x2 – 4x Evaluate lim 6x? + 1 . x+ x

Q: x³ In x dx

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Q: 1 Find L - cos2t t

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Q: Trigonometric substitution x = tan 0, dx = sec20 d0

A: We have  x=tan θ Differentiating both sides with respect to θ, dxdθ=d tan θdθ=sec2θ Since, derivativ...

Q: a f If f(x,y)= cos(x+y), then み %3D

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Q: Ansser?

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Q: The orthogonal trajectories ofr = a0 is, 02 +c r = 02 +c 2 In r = In r = -02 + c 02 In r = +c 2

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Q: The Laplace transform of L(sin7t) is_ 7 (s² – 7²) (s² + 7) (s² + 7²) (s² + 7²)

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Q: Write the expression as a power of  e.

A: We have to write the given expresison 10x2 as a power of e.

Q: Verify the identity : sin 4t = 4 sin t cos3 t - 4 sin3 t cos t

A: Verify the identity : sin 4t = 4 sin t cos3 t - 4 sin3 t cos t    

Q: 2х — 2 dx 1 — х? V1 – x²

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Q: Solve ,  40000y" - 81y = 0 y(0) = 4 , y'(0)= 9

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Q: Calculate the iterated integral

A: Definition used-    Double integral -                             ∫ab∫cdg(y)f(x)dxdy                ...

Q: d'y The order of the differential equation: 8 dy dx3 dx? + y = 0 is 3 2. 00

A: Order of a differential equation is the order of the highest derivative present in the equation.

Q: Use graphs to find set. (-3, 0) ∪ [-1, 2]

A: Consider the given set -3,0∪-1,2

Q: The path r(t) = (t– sin t) i + (1- cos t) j describes motion on the cycloid x=t- sin t, y = 1- cos t...

A: Given:           r(t)=(1−sint)i+(1−cost)j

Q: Solution of the following differential equation dx - = sec²2y dy will be а. у %3Dtan2x + с b. 2x =ta...

A: To solve the differential equation Use variable separable method

Q: Spirals Graph the following spiral. Indicate the direction in which the spiral is generated as θ inc...

A: Graph the given spiral r=aθ, where a = 1. From above figure, it is observed that graph is generated...

Q: The solution of the differential equation using variable separable  dydx+7secy=0dydx+7sec⁡y=0 is____...

A: To find the solution of differential equation dy/dx+7secy=0  

Q: - Match the logarithmic function with its graph. (a) f(x) = log; x (c) f(x) = -log; x (b) f(x) = log...

A: (a) f(x) =log2(x) We can see that 1.domain ( 0,∞) 2. Range =(-∞,∞) 3.Vertical asymptote at x=0 4. an...

Q: Please view the images attached.

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Q: Finding area Determine the area of the shaded region in lowing figures. y A y 5r y5x

A: The given curves are y=x   and  y=x3. Obtain the intersection points as follows. x=x3x3-x=0xx2-1=0x=...

Q: 7x Find the general solution of the differential equation (D² + 5D + 6)y= e'ª

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Q: Write each standard equation of an ellipse in a general form(Ax² + By² + Cx + Dy + E = 0). Show your...

A: Write each standard equation of an ellipse in a general form(Ax² + By² + Cx + Dy + E = 0). Show your...

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: The given integral is ∫04p9+p2dp. Let x2=9+p2. This gives  2x dx=2p dpxdx=pdp. when p =0,  x=3. when...

Q: 7x The orthogonal trajectories of y = ce'",where c is arbitrary constant. is 2x + 2C = 7y? O -2x + 2...

A: Given,  y = c e^(7x)    y e^(-7x) = c then get the derivative   dy/dx e^-7x + y {-7 e^(-7x)} = 0 thu...

Q: Fill in each blank so that the resulting statement is true.

A: We have to fill in the blanks: by substitution method, we can eliminate y by solving the second equa...

Q: Please answer the question with the steps... Thank you very much.

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Q: Use the Laws of Logarithms to expand the quantity.

A:   Use the Laws of Logarithms to expand the quantity.  

Q: dy The integrating factor of Linear differential equations + 5x + xy= 4+ 5x is_ dx

A: Given differential equation: dydx+5x+xy=4+5x

Q: Please answer the question with the steps... Thank you very much.

A: We have to construct a such bn for which limit comparison test hold

Q: Find the derivative of the following function. y= -87x2 -9 dy 口 dx

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Q: 7-12 - One-to-One Function? A graph of a function f is given. Determine whether f is one-to-one. 7. ...

A: 7. We know that if no horizontal line intersects the graph of the function fin more than one point, ...

Q: Use the guidelines of this section to sketch the curve   y =sin x /( 2 + cos x )

A: Given: y=sinx2+cosx graph of given function can be drawn as below

Q: Suppose a + 0 is any real number. (a) In the expression a", which is the base and which is the expon...

A: Given: a≠0. (a). In the expression an base is a and exponent is n.   (b). If n is positive integer t...

Q: 3.3 Find the sum of series. 1 + .. 1.2 3.23 '5. 25 7.27 1 +

A: Consider the given: 11·2-13·23+15·25-17·27+⋯ The above series can be written as: 12-13123+15125-1712...

Q: Find f[g(x)] and g[f(x)] for the given functions. f(x) = - x° +5, g(x) = 4x + 6 %3D

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Q: If x+2a is a factor of x5-4a2x3+2x+2a+3  find a

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Q: a. 15/T 1 8 55/2 b. 15/T 1 8 c. 15/T 1 8 55/2 d. 15 1 8 5/2

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Q: The order and degree of the partial differential equation respectively 6 9. dz + sin x xy is ду О 6,...

A: Consider the given partial differential equation. Order of the partial differential equation is the ...

Q: A solution for the differential equation xdy+ ydx=0 1S O a. y=n x+C O b. In y=-x+C O c. In y=ln x+ C...

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Q: Find the limit, if it exists.

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.