Find lim t→ 1 1 - cos2 Int 0(0.20 를 를) 0 <00,2,1> O <∞, 2, ∞ > t ./t+7, t-1 t2 − 1

Q: Show that d (x + 1)? 1 (을 tan 'x + t In dx (1 + x)(1 + x²) x? + 1

A: The given function is

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A: Given equation is fx=0 where f(x) is defined by fx=sin2x+cos3x+x2  Given initial solution is x0=-0.5…

Q: In (*-") l+V1-x2

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Q: Use the following information to sketch the graph of a continuous function with the following…

A: The given conditions are : (a) f-3=5, f0=2, f3=0 (b) f'x&gt;0 on -∞,-3∪3,∞and f'x&lt;0 on -3,3…

Q: lim x → 1- INT(x + 4) =

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Q: Let G(z)- sec 0 de for z in [0, 1]. Find G" (z).

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Q: let it be 2= f(x,y) and Y=tan' () and X = === In (r²+5²) Prove that fxx+fxy= (y² + S) (fr+fso)

A: We have to prove

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Q: 25 (6x + 5)³ But Do NOT use the Quotient Rule. a) Let f(x) = = f'(x) = Find f'(x). b) Let g(x) = 6…

A: We have to find the firstd erivative of the given functions.Recall some basic formulas: ddxxn=nxn-1…

Q: d) S x?cos (x) dx 2 a) Find f' given that f(x) = cos' (3x+1) %3D sin3x-sin 6x b) Evaluate lim x-+0

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Q: 10) )Eind fCx) if f Gx)= arc sin Se 0.00

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Q: Express the limit as a definite integral on the given interval. [3(x)³ - 7x*]4x, 2 lim i = 1 dx…

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Q: 31) Find the shaded Area A between two curves ftop(x) = 6 – x2 and gbot(x) = 2, over [0, 2] as shown…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: y' + y" = 2x²y 10y' - y = ex 2 tanh(y)y′ +2xy+3=0 y” = tanh(y/x)

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Q: S(x) 르 arcsin (금x + 1) -3 Let f '(x) = . a Find f' (x) giving your answer in the form TV (bx(x + c)…

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Q: 6. dx = x + 4x + 5 (A) arctan(x + 2) + C (B) arcsin (x + 2) + C (C) In|r*+ + 4x + + C 1 (D) + C x° +…

A: Proceed as shown below...

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A: Given: y=ln9tan-19x To find: y'tan-19x=?

Q: Suppose f (x) =5"sec2(5*). Evaluate: tan (5*) + C In (5) (A) 5*. tan (5) B +C In (5) In (5) · tan…

A: Put 5x=t then integrate it.

Q: 5 Find *: (a) y = cos(11x + 2x) dy

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Q: P2: |(e* sin x + x In x) dx

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Q: if f' is continuous, f(3)=0, and f'(3)=7, evaluate lim x to 0 f(3+5x) + f(3+6x)/x

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