3. State the domain of each of the following using interval notation. a) y= 5+log, x b) f(x)= In (13–x)

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Q: Prove that f(x)=log(x)-x^2 +1 has exactly two roots namely x=1 and x=0.45

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Q: 6. Consider the function f Cx)=5(o+5)-25 if X#し if xfO D.IS fCx) continuous at X-0? EXPlain

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A: Consider the given function as fx=x3+ax+b

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Q: 10. Consider the following function. 1 x } x > Find the values of a and b that make f(x)…

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Q: (B) Verify the Mean Value Theorem for f(x) = ln(4x + 1) on | 0,

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A: Given, H(x)=25-x2we have to prove that the given function is continous on the interval[-5,5]…

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A: In this question we will use basic of calculus i.e concept of continuity and differentability. We…

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A: Given that: f(x)=e-x

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Q: Show that the function is continuous. f(x) = log2(x2 + 1)

A: Consider function  fx=log2x2+1   x fx -4 4.087 -3 3.322 -2 2.322 -1 1 0 0 1 1 2…

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Q: Given F(X)= ×2_x+1 if ×ン Find the uaIue oFF(2) -f (o) an

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A: For concavity we need second derivative.

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A: F is a branch of f on  domain D id F is a (single valued) continuous function on D and if for all z…

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Q: Find the constants "a" and "b" so that the following function sin 2x, if 0<xs. f(x) =- lax + b,…

A: Given f(x) is continuous and differentiable at x = π/6

Q: Graph the function f(x) = 2csc r over a one-period interval.

A: The given data is: fx=2 cosecx      (1) To graph the function over a one-period interval.

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Q: Solve the problem in a paper and upload as pdf document If f(x,v) = log,(3x), Verify fxy=fyx ху

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Q: - 35) Prove that if y=flx)is continuoUS and flx1= 0 when x is a rational number, then f Lx)=0 for…

A: The objective is to show f(x) =0 for all x belongs to R.

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Q: Aen vity # 2 BLs auss ME! t) flx):1 Xスー 2.

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Q: consider a function f:lo 11-» R. and etheruoise iff RELmaan amntegrable DY not A=3+1

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A: Given that: F(x)=∫17xe-t2dt

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Q: exists depends on as long as tť? <

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A: Given: f(x) = ln(2x+xsin…

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Q: Q2: Is the function f(x) = sin x -2x + x' odd or even Odd function C Even function C Not of all O

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Q: a) Suppose that f(x) = 4x if x<-1 = cx + d if – 1<x< 2 = -5x if x 2 2 Find values of c and d such…

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Q: h(x) = (5x-1 d) m(x) = (4x² – 9x} %3D

A: Product rule of differentiation: u·v' = u·v' + v·u'   ddxxn = n·xn-1 ddxf(x)n = n·f(x)n-1·f'(x)

Q: 1)Differentiate the following f(x) = x³In (3x? – 2x + 7) esin (x) g(x) : x² – 1 h(x) = log,(x + 1) +…

A: " Since you have posted a question with multiple subparts, we will solve first three question for…