Suppose f(x) is continuous for all x and positive for all a except at x = and/ f(z) dz converges. Select the integrals that will definitely converge. P f(x - 3) da f(x) dx (f(=) + 3) dz | af(z) da O None of these are guaranteed to converge.

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A: To find the first derivative of y using the given equation.

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A: We have to evaluate these integration by assuming some terms who convert it in simple integral. 

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A: see below the answer and calculation

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A: Solve by integration

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A: Given that          y = 5 sinx + 2 cosx  Here we have to find dy/dx .

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A: a)     an=13n-1 b)        an=(-1)n-13n-1⇒an=(-13)n-1

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A: Solve the equation 2cos23x+sin3x=1

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A: A function f(x) is continuous at x=a if and only if limx→a+ f(x) = limx→a- f(x) = f(a).

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A: If f(x) is defined and continuous on the open interval (a, b) then there is a point on this interval...

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A:

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A: As per our guidelines we are supposed to answer only first three parts.kindly repost others parts as...

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A: topic - mean value theorem

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A:      

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A: Topic:- application of integration

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Q: 2 5. lim x→3 \x – 1 х2 — 1, 2 |

A: Follow the procedure given below. 

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A: Given query is to find the velocity at given time.  

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A: answer is following-

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Q: 1 sec x sin x CSC X cos X tan x

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A: Given query is to find indicated composite function and it's domain.

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A:

Q: 4. If x - xy + y = 1, find y' 3x2 a.): b.) 1-3y? c.) x-3y2 d.) +3y?

A: Using chain rule of differentiation

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A: Follow the procedure given below.

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Q: Determine the domain and range of the following function. х-1 g(x) = V16–x²

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Q: 1. d'y_dy - 42 + y =r²-2t +3 dr dt 2. y"-7y'=(2x-1)sin 2x 3. y'-5y=xe" – xe*

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Q: 6. x sec x tan x dx

A: Let's find. 

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Q: ITEM 182 Logan drew the path on this grid. How many units long is the path? A. 9 units B. 8 units C....

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Q: sinx 3. f(x)=(x)'

A: Given: f(x)=xsin xTo find the first derivative of the given function Formula: (uv)'=uv'+vu'ddx(sinx)...