Some say I csc(x) dx = Ln|csc(x) – cot(x)| + C, while other say that [csc(x) dx = -Ln|csc(x) + cot(x)| + C. Show that these are the same.

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A: 4) a) gcd(200,277)b) gcd(1001,1331)

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A: ∬xdxdyWhere R is the region bounded by y=0,y=1,x=2 and y=xy≤x≤20≤y≤1

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A: given matrix

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A: I=∫sec2⁡x1+tan⁡xdx

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A: By using a suitable change of variables to determine the following indefinite integral.

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A: To find the correct option which can be differentiated using product rule

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A: domain  : Put Similarly,  put

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A: given system of equation

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A: We need to start converting the given equation to standard form by identifying the like terms and…

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Q: (1) If f(x) = x, then f'(x) = (2) If g(x) = -8x, then g'(x) 1 (3) If h(x) == then h'(x)

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Q: K The total cost (in dollars) of manufacturing x auto body frames is C(x) = 80,000+ 500x. (A) Find…

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Q: 4. Solve the following initial value problems using the Laplace Transforms. (a) y" - y' - 2y = 0;…

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Q: Verify that (sin(0) csc(0))+ (cot(0) tan(0)) = 2

A: We have to verify,

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A: Total coloured balls= 22We have to remove all the balls one at a time.

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A: Conic section.

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A: The temperature T is given by

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A: An exponential or logarithm function cannot model the graph, because the graph is not monotonic.

Q: 11. [(5+ se + secx tan x-sec² x) d=

A: The given integral is 5+secxtanx-sec2x

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A: y=16-x,y=3x+12,x=-1

Q: Differentiation Using Graphs Example 5: The graphs of f and g are shown below and consist of line…

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Q: Use the figures to calculate the left and right Riemann sums for f on the given interval and the…

A: The left Riemann sum∫abf(x)dx≈Δx(f(x0)+f(x1)+f(x2)+⋯+f(xn−2)+f(xn−1))Δx=b−an.

Q: Find the indicated angle 8. (Use either the Law of Sines or the Law of Cosines, as appropriate.…

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A: P(x)= x4 -8x3 +22x2 -24x+4

Q: 3. π/3 S 4 sec 0 tan O do -π/3

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Q: [1 0 1] Find the inverse of the matrix C = 0 1 1 using 2 1 4 cofactors. Show all your work.

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Q: Evaluate the indefinite integrail. (Use C for the constant of integration.)

A: The given integral is sin(√x)/√x

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A: Given , the differential equation, y = 4 when x=0We find the particular solution of the above…

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Q: 83. Calculate [ sec² sec² x tan x dx (a) Setting u = sec.x. (b) Setting u = tan.x. (c) Reconcile…

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A: Recall:

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A: The given derivative funcion .The aim is to find the function for which the function passes through…

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A: