1. Evaluate the definite integral S ,2 C (9x² + 5)dx by the limit definition.

Q: 02: Let f(x)= x' – 7x+ 2, 0sxs1. 1. Show that f(x) has exactly one real root in the indicated…

A: Answer

Q: Determine the limit of f(x) as x approaches 2. * 51 f(x) 4- 5 4 2 -i 0 i 2 3 4 5 1- -2 3 5+ 3 1 DNE…

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Q: Q5) A) Graph the curve Y= - 2x (x -4)(x + 6)(x - 2) between the value of x (0, 41. then find the…

A: y=2x(x-4)(x+6)(x-2)

Q: Let f(r) = In r Find and simplify f"(x).

A: Please refer the attached image for complete solution. THANK YOU.

Q: 9. Use the Intermediate value theorem to show that f(x) = 2x( – 3 has a zero in the interval [1,2].

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Q: 2 2. Express the limit lim E(-1+4): as a definite integral. DO NOT Evaluate it. i=1

A: The given limit is: limn→∞∑i=1n-1+2in2n To express the given limit as a definite integral.

Q: otf{(16-x*)dx . b. Use the limit definition to find the exact value of

A: Using limit definition calculate given integral

Q: Find each limit f(x, y) = √y( y + 1)

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Q: f(x+h)-f(x) 2. Evaluate h If a. G) f(Vx) b.

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Q: Evaluate | re dx by changing from x-limits to u-limits. xet

A: Explanation of the solution is given below...

Q: For the function Hlo>x'tle, fnd a)flxth) 5bf(xth)- flx) c) f(x th)-f(x)

A: Given: f(x)=x2+6 To find: a) f(x+h) b)f(x+h)-f(x) c)f(x+h)-f(x)h

Q: Let f (x) = 2x + 3. Compute R6 and L6 over [0, 3].

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Q: Which graph corresponds to the function given? h(x) = {x², x 1

A: Here we have to draw the graph of the function.

Q: If f is a function defined from R to R, is given by f(x) = 5x - 3 then f -(x) is given by %3D -- 20…

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Q: 1. Use the limit formula, and showing all work, find f'(x) for f(x) = -3x³ + 2x -1.

A: To find the differentiation of given function.

Q: =) Which of the following functions are and /or IZI> 2: हन ii) 2²1 Z-√2+4 analytic in IZK< 2

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Q: x if x < 0 F(x)=sin(x) if 0 < x≤ 3 1 if 2 < x lim_ f(x) =? lim f(x) =? lim f(x) =? x-1- lim f(x) =?…

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Q: 3) √³/₂2 5 - dx -2 2x-1

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Q: c) Which of the following functions are analytic in 121² 2 2: 42²26649 (ii) Z²-1 Z-√√Z²74

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Q: Sketch: f(x) = [x + 2]] − 1, on [−2,2]

A: We have to draw the graph

Q: Use limit definition to find f'(2) for the function, f(x) = 3x? – 4x + 1-

A: fx=3x2-4x+1 substitute x+h for x fx+h=3x+h2-4x+h+1 fx+h=3x2+2xh+h2-4x-4h+1 fx+h=3x2+6xh+3h2-4x-4h+1…

Q: 5. Is the function given by g(x) = 4x³. 6x continuous on R?

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