Find the equation of the tangent line at the given value of x on the curve. y + xy? - 5 =x+3y; x= 3 y = 0

Q: Using appropriate trigonometric substitution, dx xV4 - x2 is transformed to 1 S csc 0 de cos e d0 2…

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Q: 3) i.- Given the IVP: y" +3y-4y = 20, y(0) = 0, y (0) = -5. %3D %3D | A) Use the Laplace transform…

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A: This question can be solved using the concept of limits.

Q: x3 + x2 – 5x + 15 dx 5. (x2 + 5)(x² + 2x + 3)

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Q: Use the Integral Test to determine whether the series is convergent or divergent. (If the quantity…

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Q: The particular solution y, of the differential equation y" + 4y' + 4y = 3x? + 1 is (1/8) (1-2x+6x^2)…

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Q: The general solution of the fourth-order differential equation y() + y" +y"-0 is: y=c_1 +c_2…

A: The given differential equation is y(4)+y'''+y''=0 ................................... (1)  Let…

Q: To prove that 2 dx 1+ (In x)2 + In x+c = 2 In %3D X1 + (In x)2 we use the substitutions U = Inx then…

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Q: = e3 + C is the general solution to the differential equation: y' = 3y. Select one: O True O False

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Q: 5. Consider the two curves r= / cos(0) and r= V2 cos(0), -T/2<0ST/2,whose polar plo 0.6 0.4 0.2 0.2…

A: Here, the given curves are: r=cos θ &amp; r=2cos θ

Q: - Find the point of tangency and the equation of the tangent line passing through the point p(-4,-2)…

A: Given: Now, f'(x)=-3-2x. At (-4, -2), slope = -3-2(-4) = 5. So, the equation of the tangent line is…

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Q: 3y + 2y Solving by variation of parameter y" Wronskian W is: 3e*cosx, the value of |

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Q: Given f(x, y) = 3æ'y- 8ry. Compute: www dy?

A: This question can be solved using the concept of partial derivatives.

Q: Part 2: Differentiate the following functions. Show your complete solution. 1.) (x) = (x +3x)1000…

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Q: 4. State and prove the law of sines in triangles. 5. Prove lim,0 V2r + %3D 6. Figure out the…

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Q: The terms of a series are defined recursively by the equations az = 5 5n + 2. an. an+1 4n + 11…

A: Here, the given series has: a1=5, an+1=5n+24n+11an

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Q: Use Newton's method to approximate a root of the equation 5x' + 6x* + 2 = 0 as follows. Let æ1 = 2…

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Q: Find the general solution to the trigonometric equation (2 cose - 1)(tane + 1) = 0 function value,…

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Q: A) lim x→3−    f(x)= B) lim  x→3+    f(x)= C) f(3)= D) Determine whether the function f is…

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Q: man wishes to use 100 feet of fencing to enclose a rectangular garden. Determine the maximum…

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Q: Compute the partial derivatives: ,2 z = In(x² + y³) az dy

A: Use partial derivative

Q: Problem #2: Differentiate f(x) = [(4x³ – 1)(8x² + 6x – 3)]° and solve f'(2). %3D Solution: Reason:

A: To differentiate the given function.

Q: To prove that dx In /1+ (In x)² + In x + C x/1+ (In x)2 we use the substitutions

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Q: Find the length of the curve 7(t) = (4 cos(3t), 4 sin(3t), 4t) for – 4 <t < 2 Give your answer to…

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Q: 3. Compute the area bounded by the limacon r(0) =1+2sin 0 excluding the area of the inner loop.

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Q: Use the Integral Test to determine whether the series is convergent or divergent. -2n ne =1 Evaluate…

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Q: Using appropriate trigonometric substitution, dx xV4 – x2 is transformed to J csc 0 de cos e do the…

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Q: Use the Integral Test to determine whether the series is convergent or divergent. (If the quantity…

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Q: Find the derivative of f (x) = 1+ er e* A. ex+1 C.E (e*+1)² E. None of these В. ex+1 D. (1+ e*)²…

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Q: The following telescoping series 1 sin-1 sin -1 n + 1 n=1 converges to 3 converges to= the above the…

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