Find the length of the following parametric curve. x = 6 + 916, y = 5 + 6t°, 0

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A: Given: F(x) = sin3xcos5x We know that  We have to find ∫sin3xcos5xdx Let , I=∫sin3xcos5xdx

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Q: Find the equation of the tangent line at (2,2) on the curve x² + xy + y² = 3

A: Topic = Derivative

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Q: Which of the following is the power series representation of 1 (1 – x)² п-1 nx n=1 8. xn+1 n + 1 n=0...

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Q: dx 2xy-3y2 _14. tan*y – 2 tan y +1 = x N. dy (y-x) _15. secy + sec x = tan y dx 2x dy y sin x-cos y ...

A: 14) tan2y-2tany+1=x(tany-1)2=x Dfferentiate w.r.t.xddx(tany-1)2=ddx(x)2(tany-1)ddx(tany-1)=12(tany-1...

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Q: The vector v and its initial point are given. Find the terminal point. = (4, -9); Initial point: (9,...

A: Given

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Q: 15. Evaluate o" Sy" cos(x?) dxdy,

A: Given: I=∫0π∫yπcosx2dxdy   So, The region bounded by the lines x=y, x=π, y=0 & y=π is as shown b...

Q: Find the particular antiderivative that satisfies the following conditions: dy/dx=6x+8x√3;y(1)=5.dy...

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Q: Find the points on the curve  y = 2x3 + 3x2 − 12x + 6  where the tangent line is horizontal.

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Q: Solve the stated IVP using the method of undetermined coefficients. y” – y’ − 12y = 10e^5t , y(0) =...

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Q: f"(x) = 13r- (x²-1)a 2.f(x) = f'(x) = r* +1) 4x (x²-1)2 Determine the intercepts. Determine the equa...

A: f(x) =2x2x2-1Intercepts:x=0, y=0(0, 0),y=0, x=0X and Y-intercept: (0, 0)Asymptotes:x2-1=0x=1, x=-1  ...

Q: Test the series for convergence or divergence. TT 17. 2 (-1)" sin - n=1 n

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Q: Determine the intervals of concavity for the graph of the function f(x)= xe^x. ( Enter your answer u...

A: The graph is shown below::

Q: The velocity of a car is f(t)=7t meters/second. Use a graph of f(t) to find the exact distance trave...

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Q: Write the equations in spherical coordinates 3x+4y+7z=1

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Q: 3. Determine the exact value of f"(0) for f(x) = (cos5x + 5x²)*.

A: Given 

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Q: Consider the parallelepiped with adjacent edges u = 8i + 2j + k v = i+j+ 2k w = i+ 3j + 4k Find the ...

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Q: 1- Find the area of the region enclosed by the cardioid r =1+ cos 0

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Q: xsin-1(x) is If x =0.1 and y = 0.11, then value of C in the antiderivative of F(x) = V1- x?

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Q: dx dy 1.65. dt Given y = x. Find when y = 6 and dt %3D dx (Simplify your answer.) %3D dt

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Q: d 1) a = (a & b nonzero real numbers) dx

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Q: sin x 5. Use series to evaluate dx .

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Q: x = 0, y= 1, y = e4 %3D x =-,

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Q: Antiderivative of a Function 12. S(t - 4)² dt

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Q: 1which Statement is true? A incn) absolutely. Sinc) converges combergeng because converges lim. Siっc...

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Q: Write the equation for he function graphed below. Use smallest deg 7. 5- 4- 2- 10-9 -8 -7 -6 -5 4 -3...

A: Find your answer below 

Q: Find the set of solutions for the linear system 3x1 + 4x2 + 5x3 7 || 5x2 + 8x3 -8 Use s1, s2, etc. f...

A: Find your answer below 

Q: Gren thint sin (A+i6) = xtiy, 28 Prove that, 9父+ =1 snh'B 1) x essec?A -y' sec'A =1

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Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the...

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Q: 1. 72 ecos.x sin xdx

A: As per our guidelines we are suppose to solve only first question if the multiple questions are post...

Q: 16. а — - (V3, 1), ь %3 (0, 5) b = (0, 5)

A: Given query is to find the angle between the Indicated vector.

Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answers a...

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Q: Show that every member of the family of functions y = (ln x+C)/x is a solution of the differential e...

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Q: Determine whether the planes are parallel or identical. -7x + 4y – 9z = 5 14x - 8y + 18z = 9 The pla...

A: Here we have to determine whether the planes are parallel or identical.

Q: Sondere ebch exprO sSn to G sngle logarithm 3. 2. 3. + log qfu + lay a to 3.

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Q: Ay Use the given graph of y = f(x) to find the intervals on which f'(x) > 0, the intervals on which ...

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Q: d 4) (1+ x)* = (Logarithmic differentiation) %3D

A: Given, d/dx (x+1)x We can find it by substitution method

Q: Evaluate: /sin(Vx)dx 2/x sin(/x)+2cos(/x)+ C B2sin(x)-2/xcos(x)+C 2/xsin(x)-2cos(x)+C D None of the ...

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Q: 1 2 3x2

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Q: Determine the limit of the sequence or show that the sequence diverges by using the appropriate Limi...

A: We can solve this as follows:

Q: te ove (2y – x) dx dy 16-y2 12. -4

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Q: (x²+6y²)dx – 4xydy=0

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Q: dx + (x – y + 2)²dy = 0

A: The objective is to solve the differential Equation. 

Q: Find the area of the surface generated by revolving the curve x in the interval 2 Osys In6 about the...

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Q: 6. A population of fish is living in an environment with limited resources. This environment can onl...

A: Given is differential equation in P (a) In this part by just looking at the differential equation we...