sin(x) 1- sin? (x) 3. Evaluate the integral O 2ln|1 - sin2(x)| + C O -csc(x) + C sec(x) + C O None of these

Q: 7. Lonsider the plane through the three polnts Po(1, 0, 0), Pi(1, 1, 0), P2(0, 1, 1). 7.1. Find an…

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Q: Compute the partial derivatives: 5x dz dz

A: Given query is to find indicated derivative.

Q: Using decomposition into partial fractions, 4x2 + 2 dx x(x2 + 2) is equal to In/x (x² + 2)| + C…

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Q: 3. Which of the following integrals cannot be evaluated using a simple substitution? 1 xp- x +1 ,4 1…

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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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Q: 12. Consider the region R bounded by the line y = 37 – 7x and the parabola y = 27 – x² . %3D Find…

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Q: Find the linearization of the function f(x, y) = V61 – 3x2 - 1y? at the point (4, 2). %3D L(x, y) =

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Q: Problem #2: Differentiate f(x) = [(4x* – 5)(3x² – 9x – 5)]° and solve f'(2). (5 pts.) Solution:…

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Q: I -4 () Draw the graph of f(x) 6.

A: Using graphing calculator,

Q: An inverted pyramid is being filled with water at a constant rate of 60 cubic centimeters per…

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Q: Suppose the position of an object moving horizontally after t seconds is given by the following…

A: Given equation is quadratic so accordingly draw the graph and then solve .

Q: The integral X dx Vx2 – 4 3

A: To evaluate the given integral.∫12 xx2-43 dx

Q: On the circle x² + y² = r², find y". r2 A. y" C. y" = y - x3 E. None of these -x² - y2 В. у" D. y" :…

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Q: 1 What is the instantaneous rate of change of Y= at x = 2? - o-1 4 O none of these -1 -1

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Q: Find the following limit or state that it does not exist. x - 4x +3 lim X-3 x-3

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Q: Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b). If the…

A: We have to check if Mean value theorem can be applied or not.

Q: Given that f(x) = x² - 5x + 6, evaluate the function fla +b) - fla). 2a+b-5 b-5 2a+b+1

A: Simplify the expression for the given value of x

Q: Find f. f"(t) = 5et + 4 sin t, f(0) = 0, f(1T) = 0 f(t)

A: topic- differential equation

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

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: Solving by variation of parameters y" + 2y' + y = e*the general solution is: c_1 e^(-x)+c_2…

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Q: In two or more complete sentences, explain how to find the third term of the expansion of (2x+y)4.

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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 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: cos(xy) + secy = 5

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Q: If h(x) = V6 + 5f(x), where f(2) = 6 and f '(2) = 3, find h'(2). %3D h'(2) = %3D

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Q: Evaluate the given integral. [ 2x?sin(4x)dx

A: The given problem is solved below in detail.

Q: b) sec(arcsin x2+4, 以a sin g 孙 OPP Los : als hyp a-t6-cと とい ))Not how sec = x-Vxty %3D exponent…

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Q: Activity 1. Match the functions in Column A with their corresponding antiderivatives in Column B.…

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Q: The technique used to prove that x4 x3 , dx =- 2x + 2vZtan- ( 2/2tan + C x2 + 2 3 is Long…

A: We have to find the method

Q: 4. Let R be the infinite strip between the x-axis and v= xex x20. Determine if the area of R is…

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Q: The polynomial of degree 4, P(x), has a root of multiplicity 2 at a = 2 and roots of multiplicity 1…

A: Root of multiplicity is defined as the number of times each roots appears.

Q: Su(u² + 3) du

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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: evaluate the integral - sin (x) dx (x) 1- sin |3|

A: The given integral,      ∫sin(x)1-sin2(x)dx

Q: A population of bacteria is growing according to the equation P(t) = 2000e0.05t. Estimate when the…

A: Given query is to find the Indicated time.

Q: The average rate of change of y with respect to x over the interval [0, 3] for the function y = 3x…

A: The function y=3x+2 over the interval 0,3

Q: A. Evaluate the following integrals. 1. S(Vcos x + sin x)*dx xp. 2. S cos 3x dx

A: LetI=∫cosx+sinx2dxI=∫cosx+2sinxcosx+sin2xdxApply the Sum RuleI=∫cosxdx+∫…

Q: Use the figure to find the exact value of the trigonometric function. Find cos 20. 29 21 20 41 841…

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Q: 1 ): The vectors 2 and form a basis the vector space R'. Select one: O True O False

A: Here we state whether it is true or false.

Q: 1. For the curve x²y? = 25 at (-1,-5), find the equation of the normal line. %3D

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Q: Find an equation of the plane. The plane that passes through the point (−2, 3, 2) and contains the…

A: This question can be solved using the concept of planes in three dimensional geometry.

Q: Part a: Assume that the height of your cylinder is 4 inches. Consider A as a function of r, so we…

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

Q: 4.) f(x) = etinlx)+cos (x) 2+4x+4 5.) (x) = = 6.) S(x) = +r-s)(ar-7) 622-131+7

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Q: Using the substitution x = sec 0, dx S: J x2Vx2 _ 1 where x > 1, is equal to

A: We can find the answer as below.

Q: 1) Calculate 21+v3i

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Q: 4 Consider the following geometric series: 2 + 8. 16 + ... Identify a and r, find a formula for the…

A: solution:-2+43+89+1627+...first term, a=2common ratio, r=8943=23general term, an=arn…

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…

Q: - f(æ) = Where is %3D discontinuous? x2 + 3x – 18 - o f(x) is continuous everwhere O 3 O-3 and 6 O-6…

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Q: Convert the equation to the standard form for a hyperbola by completing the square on x and y. 9y-4x…

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