Find the constant a such that the function is continuous on the entire real line. Ssin x g(x) = if x < 0 5x if x 2 0 a 3D

Q: (a) Find the equation of the tangent line at A. (b) Find the area of the shaded region enclosed by…

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Q: 2. Find the general solution of cos x dy + (y sin x – 1) dx = 0 %3D

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Q: find the Langth of the are Ve Siesinzo from to o-52

A: Given:        r=1+sin2θ   Interval is 0,2π  Length of the arc of the curve is given by…

Q: solve

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Q: Determine the center of mass for the region bounded by the following y=x^3 and y=√x.

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Q: A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.4 cm/min.…

A: We know volume of a sphere of radius r is, V= (4/3)πr³ Doing implicit differentiation on both sides…

Q: 7. (a) y(4) when y 2ln 30 1 (b) y() when y= %3D In 2t %3D

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Q: f(X) ex finathe cn'nical numbers of f O de remine whethereacn is a1ocaimaximum, 1ocalminiumum…

A: Critical points

Q: (メ+ッ)dx + (x4ッ)dy =0 dx dy x yz x?y

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Q: 7. Evaluate the following: (2x2y 2+2y)dy dx A. 3.0 B. 5.4 С. 2.3 D. 4.9

A: Given query is to find the value of the integral.

Q: Evaluate the integral 1

A: We can solve this as follows:

Q: - y = x' 3 from x=-1 to x=2 %3D

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Q: 1. Write T if the given statement is true with respect to the underlined term(s); otherwise, write…

A: 14.   False  15.  False explanation 14. Since the range of cos(x) = -1 to 1 And for improper subset…

Q: 8. To find the derivative of y = cot* (2x), which of the following is the appropriate value of u? A)…

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Q: General solution of x dy = (2xex – y + 6x2) dx %3D

A: The given equation is: x dy=(2xex-y+6x2)dx That can be written as:…

Q: Q3: Find f(t) ( Inverse Laplace Transform )of the following functions s+1 2.F(s) = s4+s2

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Q: Evaluate the following integrals. 1.) Sdv csc 3v 2.) S cot 9x dx

A: ∫5csc(3v)dvSubstitute u=3v→dudv=3→dv=13du=∫53csc(u)du=53∫sin(u)duWe know that…

Q: Homogeneou dinan Equati on Oblain the differemtial equation 1. y= 7-2x + e

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Q: dy Find Y dx (x- 2) - (2x+1)4 if y= | Use logarithmic differentiation. x=0 e2x. Vx+8

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Q: L(sin 2t cos 2t)

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Q: II. Consider the function g defined by 1 g(x, y) = cos (Tx Vy) + log3(x – y)" Do as indicated. 1.…

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Q: Suppose f(x, y) = x2 + y? where x = r cos 0 and y = r sin 0. af and Or 1, 0 = 6 Find -when r

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Q: 5 and 6

A: 5. ∫127*ln(3x)xdxSubstitute u=7ln(3x)→dudx=7x→dx=x7du=17∫12uduWe know that…

Q: ACTIVITY 2:Solve the given below. Show your complete and exact solution. 5. Given the function f(x)…

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Q: 1 11. lim, -2 Inx x-1

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

Q: (y®+ 4y³-Ay) dy y2+10 6. ,3.

A: LetI=∫y5+4y3-4yy2+10dyI=∫y5y2+10+4y3y2+10+-4yy2+10dyI=∫y5y2+10dy+∫4y3y2+10dy-∫4yy2+10dyTake constant…

Q: x + 2 x + 1

A: ∫x2+2x+1dxSubstitute u=x+1→dudx=1→dxu=dxx2=(u-1)2 =∫(u-1)2+2udu=∫u+3u-2du

Q: Find the equation for the plane through the points Po(-5, - 2,- 2), Qo(3,2,4), and Ro(4, - 1,- 2).…

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Q: Find f'(x). Given: f (x) = 5xv3x² – 4

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Q: 10) (-1

A: lets we take example 9 and 10   9 (-2) -3/2 here in 3/2 so we have to also make 2 in whole term…

Q: 8. f2*Inx dx(ו1 + In)x

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Q: Find the value of y (0.4) if y' + 0.2y = 0, y(0) = 5. Solve analytically.

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Q: Q2:Find the Laplace of the following functions: 1- cos(2t) 1. f(t)

A: We will find the Laplace Transform

Q: dy (x– 2)³ · (2x + 1)ª Find if y = dx|, e2x . Vx+8 Use logarithmic differentiation.

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Q: Find Inz3 -dz

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Q: Iy 3. cosysiny dy

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Q: 1. How to solve the values of x to find the critical values of the graph of a polynomial function?…

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Q: Find the first derivative of  y = cos4 x – sin4 x y = x3   –  x2 cos x  +  2x sin x  + 2 cos x y…

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Q: -2 2 7e" + dy -5

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Q: .

A: We will find the temperature.

Q: 3. (a) y(8) when y=cos 2x 2 (b) y(9) when y=3 cos t 3

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Q: : Use PARTIAL FRACTION DECOMPOSITION to find -1 dm т2-6т-7

A: We have to find integrating using partial fraction.

Q: 15. Differentiate 4y³ with respect to x. A) 12y? B) 12y C) 12y2 dy D) 4y2 dy dx dx 16-17. Find the…

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Q: The matrix given is in reduced echelon form: 1  0  5  -2 0  1  4   1 0  0  0   0  Write the…

A: To write the matrix equations.

Q: s+1 1. F(s) = 2.F(s) = s4+s2 2 (s +2)'+n?n²

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Q: sec(2) tan(z) – 1 dz 1 dz

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Q: A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.2 cm/min.…

A: We know that volume of spherical snowball V=43πr3 Differentiate w.r.t.'t'…

Q: dy Use Picard's method to solve dx -xy, y (0) = 1 Find y3(1)?

A: Given :dydx=-xy =f(x,y)y(0)=1

Q: Find the vertices, the foci and asymptotes of the following hyperbola. 4x? – 49y? = 196 Vertices :…

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Q: 2r³ – 4x² – x – 3 dx x² – 2x – 3 in |x + 1|+ 3 In|x – 3| + C in Ix + 1|- 3 Inlx – 3| + C Option 1…

A: Given