Using integration by parts, uV- V du cone for j 3*crc'(3x) sin C3x ) dx solution. dv = du = V =

Q: (c) z = 5x + 2y where x = 1+ 2cos(t), y = sin(t) – 3 andt = dz answer: dt dz 2cos(t) – 10sin(t), = -...

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the remain...

Q: Using the graph find the following: (6.5) a. lim f(x) e. lim f(x) X-4 (4.2) f. lim f(x) (2). (6.2) b...

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Q: 3. lim (3 Vx + 9/

A: This is a problem related to limit of the function. Based on the general formula of limit or using L...

Q: 1.)When m is odd, we can integrate sin" (x) dæ by letting u cos(a). Why does have to be odd for this...

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Q: x1 x + dx

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Q: Determine whether the series converges. 00 Σ k=1 V7k – 1 O The series converges. O The series diverg...

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Q: Use the ratio test to determine whether the series converges or diverges. If the test is inconclusiv...

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Q: Find the inflection points of each of the given curve.  y = x3 – 3x2 + 4

A: ⊙a function y=f(x) is said to have inflection point at x=a, if its second derivative i.e. d2ydx2 cha...

Q: d²y 2. Find the second derivative of x? – 3xy? + y3 = 15 dx?

A: The given equation is; x2-3xy2+y3=15.

Q: If h(x) = 5 – 4x", find h' (2). Use this to find the equation of the tangent line to the curve y poi...

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Q: +2 7. (i) Show that A(c) !! (-2)* (ii) Given the previous part, find a closed form for >

A: Find your answer below 

Q: Evaluate f w?sin(10w)dw using integration by parts W

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Q: Find the points at which the following function is discontinuous. (2r2 + 4 ifx 4 Select the correct...

A: The given function is f(x)=2x2+4if x<-56x2+2if -5≤x<42x+90if x≥4 Since polynomial functions ar...

Q: 1 — п b. 2n + 1 n=1

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Q: Find the solution of the given initial value problem in explicit form. sin(2x) dx + cos(6y) dy = 0, ...

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Q: For the following items, consider the sequence {()"-}. 1. What are the first five terms of the seque...

A: We have to find 1st five point and draw the graph as well as the property of sequence

Q: plane is flying directly away from you at 500 mph at an altitude of 3 miles. How fast is the plane's...

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Q: Find the inflection points of each of the given curve.  y = 5x – x5

A: Given :y=5x-x5

Q: Evaluate

A: Please refer to the image below

Q: sin –9xdx

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Q: 12

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Q: ーX- 3, -3x2 + 2x - 3, x> 1 x< 1 f(x) = %3D Determine which of the following statements are true. Sel...

A: We will find left hand limit (L H.S.) and right hand side (R.H.S).

Q: 1 dx x/1+ x6

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Q: y par e for JTx (inx)? dx. wtioni dv = %3D

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Q: What is the general solution to the differential equation 2e* cot(y) dx – (4 + e*) csc²)dy = 0 ? (4 ...

A: Here, the given DE is: 2excot(y)dx-(4+ex)csc2(y)dy=0

Q: Find the length parameter of the curve r(t) = with base point at ( 7, 0, 0 ).

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Q: S (x +) dx 2 X.

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Q: For the next three questions, consider the differential equation: y" – 2y' + y = e* arctan r

A: Particular Integral

Q: Find the area in the first quadrant that is inside the circle r = 4 sin 0 and outside the lemniscate...

A: We need to find area.   NOTE - As per our guidelines we can solve one question so please upload othe...

Q: Use any method to determine whether the series converge. 1 (a) E 'k² + 15k + 1 This series diverges....

A: To check the convergence of the given series.

Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges. I...

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Q: tio test for absolute convergence to determine whether the series co te

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Q: INTEGRAL Evaluate the following: e 20do 10. ↑ 1+ 3e20

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Q: Exercise: 1. Convert the Rectangular coordinates (-1,1, v6) to spherical coordinates. 2. Convert the...

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Q: Find an equation of the tangent line to the graph of y = g(x) at x = 6 if g(6) = -5 and g'(6) = 3. (...

A: As we know that; The slope of the tangent line to the curve is equal to the derivative of the functi...

Q: -x' + 2 Find the slope of the secant line between x = -3 and x = 3 for the function f(x) = (Enter yo...

A: Given that a function f(x)= (-x3+2)/(2x-2). And we find secant slope of line between x=-3 and x=3 fo...

Q: olve a nonlinear equation by making a change of the dependent var portant such equation has the form...

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Q: Determine the approximate root (x_r2) of the f(x) = 0.35x^4+2x^3 -x^2+0.36x +4, upto 2 iterations us...

A: f(x) = 0.35 x4 + 2x3- x2 + 0.36 x +4 f(-2) = -9.68 &lt; 0 f(0) = 4&gt;0 Hence, a root lies between -...

Q: sin n n2 n=1

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Q: Find the equations of all tangent lines to the graph of y=x -7 x+ 49 that pass through the origin (0...

A: Equation does not passing through origin.  Hence there are no tangent line whose passing through ori...

Q: Solve the given differential equation. All solutions should be found. dy etz + 7y dx 4.x NOTE: Use c...

A: The given differential equation,      dydx=e4x+7y

Q: asider the function f(x) = e" on [0, 2), %3D

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Q: Let F(x) = f(x) + g(x), where the graphs of f and g are shown in the figure to the right. Find F'(3)...

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Q: 6x 4. У3 y = х+3

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Q: If x2 + y2 = 100 and dy/dt = 4, find dx/dt when y = 6. (Enter your answers as a comma-separated list...

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Q: f(2) Suppose that the limit value of: lim a , what does imply? g() O a. A limit exist. O b. The nume...

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Q: If y = 3x3 + 2x and dx 5, find dy when x = 2. %3D %3D dt dt dy dt %3D

A: Given, y=3x3+2x  and dxdt=5 We have to find dydt when x=2  

Q: 7. Determine which of these positive integers are a) 1,5,7,11,13,17,19,21, 23,25, 29,31 b) 1,5, 7,11...

A: We know that  Two numbers are said to be relatively prime if their greatest common divisor is one. F...

Q: lim square root of (n + 2i) – square root of (n + i). C. O 12. Evaluate the ninfinity B.1 A. 2/i

A: We will multiply and divide by a factor which numerator a square type and will remove square root sy...

Q: Evaluate the integral below by following the steps given. 1 xp= x2 I || 6/ a.) Show that the substit...

A: Given: I=∫19-x2dx  ...1   As we know from the trigonometric identity: sin2θ+cos2θ=1 And ∫a·fxdx=a·∫f...