Which of the following is one of the correct steps to evaluate cos'x dx to obtain the desired integral. A None B / (sin²x – 1)³ cos x dx - (1+ cos 2x)³cos x dx C [ 1– sin²x)³ cos x dx D © :/(1+ cos 2x) *cos x dx 1+ cos 2x)³cos x dx (E) 00

Q: Use Newton's Method to approximate the zero(s) of the function. Continue the iterations until twO…

A: Let's find.

Q: Q2/ Fit a second -order polynomial to the data in the following table: 5 1 4 2 Y 2 8 3 4 -1 4 6.

A: We need to find quadratic equation.

Q: Remember, even if you enter an answer rounded to a set number of decimal places, if you use that…

A: Law of sines : sin Aa = sin Bb = sin Cc Given  ∠A=38.8°,  a=182.4,  b=248.6

Q: Evaluate the following integral using Partial Fractions Method: x3 + x2 y : dx x2 + x – 2

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Q: Consider the region bounded by the curve v= x2 – 1 and the x - axis over the interval [0,3]. Find…

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Q: Show that the lines L1 : x = 5 – t, y = 2t, z = 1+t and L2 : x = 1+ 2t, y = 3 – 4t, z = 5 – 2t are…

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Q: Q2: Find the integration by applying substitution method: 7 dX (X – 1)VX2 – 2x - 48

A: Given,             ∫7x-1x2-2x-48dx

Q: EValuate J s 2'as O a. 2*(sln2 – 1) (In2)2 O b.2(sln2 - 1) (In2)2 O C. 25 sp.7s (1 – Zu). + 1) In2 O…

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Q: Evaluate f s 2°ds О а. 2"(sin2 - 1) (In2)2 O b. 2(sln2 - 1) (In2)2 O C. 2* In2 O d. 25 In2

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Q: Q4) Evaluate the following integral using Trigonometric Substitutions Method: 1 - x dx 2. y =

A: To evaluate the given integral.

Q: Substitute x = 120 and y = 160 in s = x + y. (Only positive values need to be considered.) %3D 2. +…

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Q: Solve the particular solution of the equation dy/dx = 3x² - 2x, when y=2 and x=-1.

A: We can solve the given problem as follows:

Q: Q2) Solve the D.E x²dy + (3xy- 1)dx 0

A: Let's find.

Q: Q5) Find volume of body bounded by z? + y2 + x2 9.

A: Given that - x²+y²+z²=9 => (x-0)²+(y-0)²+(z-0)²=3² Clearly which is a sphere with radius,r= 3…

Q: Consider the parametric curve defined by x=3+5t and y=1+31 Over which values of , does the curve has…

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Q: Which of the following limits has a value 0? In x I. lim II. lim X-0 e* Neither I nor II. O l only…

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Q: 2.Find the indicated limit or state that is does not exist x* – y* C. lim (x,y)→(0,0) x² +y ху d.…

A: Solving

Q: Find volume of body bounded by z 0 from below and z = 4 - y from above inside y = x2 ,y = 4 .

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Q: Q3) Find the Area bounded by the curves y? = and x = 2y – y².

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Q: Evaluate the following limit: (x- 2)2 – 4 | lim If it does not exist enter DNE.

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Q: Find each of the following indefinite integrals.  c. Z (r+2)^2/r^3 dr

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Q: Find the AuRtaYe value of f(x) = x* on the intervai 2,67

A: answer is in next step

Q: Find the absolute extrema of the function on the closed interval. (x) = 7x2 + 1, (-1, 2] minimum (х,…

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Q: 5.Find all the first partial derivatives of each function f (x,y) =(2x– y)* а. 3/2 S(x, y)= (4x–…

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Q: nsider Evaluate дхду

A: Given,             z=ex3+y2To find : Evaluate ∂2z∂x∂y

Q: Evaluate: / sech[in cosr Janx dx A -2 tan-1(e cosx) +c cOsx B) None 2 tan -(e cOx) + C COSA D - 2…

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Q: write the equation of a parabola whose directrix is x = 5.75 and has a focus at (12.25, 5).

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Q: Q3) Evaluate triple integral f, L(x - y?)dz dy dx.

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Q: Let C be the line segment connecting the point p = (2,5, 0) to the point q = (0,6, –5). Find a curve…

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Q: Consider a continuous function f(x). The function has critical points at x = -7, x = -2, and x = 7.…

A: f(x) has critical points at x=-7 , -2 , 7Since f''(-7), f''(-2) is positive ⇒There is local minimum…

Q: Compute f'(a) using f'(a) = lim f(a + h) – f(@) or f'(a) = lim Tx) – J(d) for f(x) = 15x³, a = 2. or…

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Q: Solve the D.E dy -(2x /1-y2)dx = 0

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Q: find the derivative and simplify the answer sin² (esin t) + cos-{(2t3 – 5)

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Q: 1.5 3-y Q1) Evaluate the integral dx dy

A: To evaluate the given integral.

Q: 1' 1 3 (e) Show that 5 k=1 k k+2

A: I am attaching image so that you understand each and every step.

Q: Determine a and b so that the function f(x) is continuous for all values of x. jika x <- 2 sin x…

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Q: tan²x dx, can be evaluated by using trigonometric transformation . A True False

A: The given integral is: I=∫sec5xtan2xdx Use the derivarive: ddx(secx)=tan2x

Q: If Ax) = a(x-h)* +k, where a, h, and k are constants, find f"(). 2ax O 2(x-h) O ax+h+k 2a

A: The given function is f(x) =a(x-h)2+k,   where a, h, k are constant. We have to find f''(x) f''(x)…

Q: Question 5. Find the Laplace transform of the following function by using the integral definition of…

A: Given problem:-

Q: Q2) Convert the polar function r tan20 to cartesian.

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Q: The limit represents a derivative f' (a). Determine f(x) and a. 14h lim 1 h→0 (Express numbers in…

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Q: PART II. Find the derivatives of the following expression, solution must be presented. (3 marks…

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Q: Let y=f(x).Which of the following correctly defines dx [fk+Ax)-fw] a. lim Ax+xL Ax Ob. lim Ax+x…

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Q: Q2) Convert the polar functionr= tan20 to cartesian.

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Q: Apply the chain rule to differentiate the following functions. Show your complete solutions and…

A: Since, you have posted multiple questions. As per guidelines, we"ll solve only first question. If…

Q: Evaluate lim オ-5 x(x + 1). オ→0*

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Q: Vx – 8 = xy + 2

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Q: Q4) Evaluate the following integral using Trigonometric Substitutions Method: 2 y = - x dx

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Q: Σ (-1)" n=1 3-4n-1

A: topic - geometric series

Q: / sin*0 d0, factor sin*0 as (sin²o)² sin® and let sin²0 = -(1– cos20). To evaluate A True False

A: Given problem:-