Assume that f : (e)R is

Q: There is no function f(x) such that f(x) = f(x) + C. %3D

A: (1) We have the given statement as If fx and gx is continuous function then, ∫fxdx=fx+C. The above…

Q: Use this definition to find f'(a) at the given number a. f(x) = V5x + 1, a = 3

A: First we find out f'(x) then put x=a=3 in f'(x).

Q: 6. Use an appropriate substitution to prove f(r)dr = f(a + b – x)dr. %3D

A: We have to prove definite integral property.

Q: Let f : R" → R with f(x) = /1+ ||x||?. Show thatf€ C.

A: As per the question we are given a multivariate function f from Rn to R , and we have to show that :…

Q: Show that f(r) = O(|x – xo|*) and g(x) = o(]x – roP) imply f. g(x) = o(|x – xo]k+i). - -

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Q: Let f(x, y) be the function Vlxy|. Which one of the following statements is correct?

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Q: Use the Product Rule to differentiate f(s)=Vs (3- s°). |

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Q: Show that the function f(z)= Im(z) is nowhere differentiable.

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Q: f) S(2).

A: First Represent the f(x) in x to the power  form than take derivative.

Q: Let f(x, y) = x* /I Evaluate f(3, 0)

A:

Q: Consider f : R → R given by f(x) = x². What are the domain, codomain and range of f?

A: Let a function f : A→B thenDomain: set ACodomain: BRange: Values that comes out after putting values…

Q: For f(z) = V, find f'(x). f'(z) =U

A: Given:  fx=8x3 To Find:  f'x=?

Q: Find F(s). F(s)

A: We use the table of Laplace transform to answer the given question.

Q: Give an example where | f(x)dg(x) exist even through f is unbounded on [a, b].

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Q: f 'C) =7x*+7-3 ond fl0) 3D8

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Q: Let f: R" x R → R define as follows f(x,y) = a, then f is

A:

Q: Use the Second Fundamental Theorem of Calculus to find F '(x).

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Q: Use the second fundamental theorem of calculus to find F'(x)

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Q: Formulate a condition for f to be symmetric with respect to the point (a, 0) on the x-axis.

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Q: If a F (z) = xy+ i (x² – y²), what is F(-1+ 2i)?

A: The given question  is related to complex numbers.  Given F(z)=xy=xy+i(x2-y2) We need to find…

Q: If f(x) is continous on [a,b] then f(x) is differnitable on (a,b). True or False?

A: False Any differentiable function must be continuous at every point in its domain. The converse does…

Q: Let F =. Find the lin , 0 <t< 2n.

A: Introduction: If f (t) is a smooth parameterization of an orientated curve for a≤t≤b If C is a…

Q: Find f(x), if f(x)=f(x)+ƒ f(x) dx, given that f(0) = 1.

A:

Q: Why is ƒ not a function from R to R if f(x)= ½? b. f(x)= Jx ? c. f(x)=±/(x² +1)? а.

A: Why is f not a function from R to R if,  a) f(x)=1xb) f(x)=xc) f(x)=±x2+1

Q: Use the intermediate value theorem to find the value of c such that f(c) = M. c =

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Q: Given f(x, y) 70x + 60y – 2? – 3y? – xy - - evaluate f(1, 3). f(1, 3) =

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Q: 1. Why is f not a function from R to R if a) f(x) = 1/x? b) f(x) = VT? c) f(x) = ±/(x² + 1)?

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Q: If f(x) = . , then f' (x) at æ = 1 is f (r) at a

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Q: Use the second fundamental theorem of calculus to evaluate the following: x, x 20 10. [* f(x) dx if…

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Q: Use the given Information to prove that DG=FH.

A: DE=FG EG=GH To Prove: DG=FH We can write  DG=DE+EG DG=FG+GH      (DE=FG, EG=GH) DG=FH

Q: ) Differentiate f(r) = In(v²) + In(10). Hint: Think before differentiate :) you

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Q: Assume that f(z) = ez then Re(f(z)) and Im (f(z))are

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Q: For f(z) =, find dy using the definition, 127

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Q: Use an appropriate substitution to prove f(x)dr f(a + b – x)dr.

A:

Q: Suppose f(r) = (In z)e. What is f'(x)?

A: d/dx (f(x)g(x))= f(x)g'(x)+g(x)f'(x)

Q: use abs (x) for |x|, Given that f(x)=|x| and g(x)=8x−1g, calculate(a) f∘g(x)=    (b) g∘f(x)=    (c)…

A: Two functions f(x) and g(x) are given

Q: Differentiate f(x) = (a-x)(a + x) with respect to x. Assume that a is a positive constant. f'(x) =

A: Solving the problem by finding the value of the differentiation.

Q: Consider z as function of the variables x and y, it is defined by :

A:

Q: The function f(x) = is Lipshitz on ]0, ∞[. True False

A: A function  is called a Lipschitz function if f(x)-f(y)≤Cx-y for all x and y, where C is any…

Q: Use this definition to find f'(a) at the given number a. f(x) = V6x + 7,

A:

Q: Assume that we have functions f(x) and g(x) so that

A: Given functions - ∫-13f(x) dx = -1∫35f(x) dx = 4∫-11g(x) dx = 3∫15g(x) dx = 2∫-152f(x)-5g(x)dx = ?

Q: Use this definition to find f'(a) at the given number a. f(x) %3D 6х°, а %3D -1

A: Consider the given function. fx=6x5 The objective of the problem is to find the value of f'(a)  at…

Q: Find  f' in terms of g' .

A: Given function is fx=egx.

Q: de fined as F(X) = P(X f(t) for – a <x < a. - t<a

A: Here f(t) is probability density function of x.  Where -a&lt;x&lt;a.

Q: If f"(c) = 0, then f has an inflection point at c. %3D

A: Answer: True.

Q: Use FTC I to prove that if |f '(x)| ≤ K for x ∈ [a, b], then |f (x) − f (a)| ≤ K|x − a| for x ∈ [a,…

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Q: If f(x) = cos (r?) , what is f'(x) ?

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Q: Evaluate , f(x)dx given that f, f (x)dr = 4, f(x)dr = -2, and f(x)dx = 3.

A: Definite integration

Q: Let f: R" x R → R define as follows f(x, y) = then f is

A: Given that: f:Rn×Rn→R define as follows fx,y=∑xiyi¯i=1n. The objective is to determine the value of…

Q: for f (z) = z – Z where does f (z) exist?

A: