2x Let f (x) = x+3 Then f is increasing over R*. False True

Q: -1 if f(x) = xtan ,"x,find f' (/3 )by first principle

A:

Q: 2.if f (x) = x2 + 3, with domain R then f(x) has f(x) %3D O T F

A: Here the given function is f(x)= x2+3 with domain R We need to find it has inverse or not.

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

A:

Q: 67. Is the function given by g(x) 1 continuous over %3D x + 5 the interval (-4, 4)? Why or why not?

A: g(x)=1x+5

Q: Find conditions on a and b that ensure f (x) = x3 + ax + b is increasing on (−∞,∞).

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

Q: true or false  if f(x) is continous at x=a, then f(x) is differentiable at x=a

A: False.    The given statement is not true in general.

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…

A:

Q: 2. f(x) = Vx – 1 at x = 5

A: Function is continuous and differentiable both at x= 5.....for detail...go through the solution

Q: 3) Determine A and B that makes the function continuous as x approaches 0 and 1? y A x>1 x-B x<0

A: Given:           y=x2                  0≤x≤1A                   x&gt;1x-B             x&lt;0 Given…

Q: I. Is the function given by g(x)=x²-3x + 2 continuous over the interval (-4, 4)? Why or why not?

A: Function given is- g(x)=x2-3x+2 continuous over the interval (-4,4) . Wee need to determine whether…

Q: True or FalseA 1. A Step-function is continuous at every point in its domain

A: Given: A step - function is continuous at every point in its domain. To write: The given statement…

Q: 10 If f is continuous and f(x) dx = -15, evaluate f(5x) dx. %3D

A:

Q: If f(x) < 0 for all real numbers x then f is decreasing on (-o, 00).

A: Proceed as shown below

Q: 6. Use an appropriate substitution to prove f(x)dr = | f(a+b- x)dx.

A: To use an appropriate substitute to prove  ∫abfxdx=∫abfa+b-xdx

Q: x² + 1, if x < 1 3x, if x 1 is f(x)continuous at x = 1? Explain. 16 If f(x) %3D

A:

Q: Find number k so that f(z) = 10x + 8 x -1 is continuous on (-0,0). O -2 4 -4

A:

Q: 1 - t Let F(x) = dt for -o << x < +∞ t2 + 24

A:

Q: Let I be the interval disjoined from {-1,1} .Prove that the function f(x) = x+(1/x) is…

A: Given that I is any interval disjoint from [-1,1]. Let I=(-∞,-1)∪(1,∞) f(x)=x+1x To show f(x) is…

Q: +1 Differentiate the function f (x) = In +1

A:

Q: X = (1-_-_-_-)* 2 o then f(x) tend:

A:

Q: 12. Use the definition of increasing to argue that f(x) = x5 is increasing on all of R. Then use…

A: The increasing of a function indicates that the value of the function increases with the increase of…

Q: How many continuous functions f are there which satisfy (f(x))² = x² for all x?

A:

Q: Let f(x)=x²+2x if x<5 - Cx if x 25. For what value of the constant c is the function f continuous on…

A: We have to calculate the value of c

Q: If f'(x) = x² +4x. then f(x) is increasing on the interval (-4,0). Select one: O True False

A:

Q: how that: (f)=X*(-f) x(t) is even, then b₁=0, an= To

A:

Q: 3. Is the function given by (x²-4x-5, x<5 F(x)= x+1, x25 continuous at x = 52 why or why not ?

A: Given function, f(x)=x2-4x-5;x-5;x&lt;5x+1;x≥5; The objective is to tell whether the function is…

Q: 2. Let f(x) = r³, 0, if reQ if r ER\ {Q} Show that f'(0) = 0.

A: We have given a function ,  fx = x3 , x ∈ ℚ0 , x ∈ ℝ \ ℚ We need to show that , f'0 = 0 We know the…

Q: 9. If f is continuous and f(3x) dx. f(x) dx = 8, evaluate Answer:

A: Given:

Q: 3. Over which interval is the function f (x) = 1 + 2ex -3x increasing?

A:

Q: 31. If f(x) = In(x + In x), find f'(1). %3D

A: It is simple differentiation  problem.

Q: Show that the function f(x) = exp(-|x|) is not differentiable at x = 0.

A: Given function is  fx=e-x given point is x=0.

Q: 3-The function f defined by 2. Is f is Continuous at x=| ?

A:

Q: If 7x-5,x < 1 h(x) 3x2 – x, 1 < x < 3 Is h(x) continuous at (x=1)?

A: Given: hx=7x-5,x&lt;13x2-x,1&lt;x≤3 We know that any given functiony=fx will be continuous at x=a…

Q: True or False Suppose f is differentiable everywhere. Then the chain rule assures that d/dxf(f(x)) =…

A:

Q: 86. If f is continuous and f (x) dx = 4, finc

A: Given that: ∫09f(x)dx=4

Q: True False Suppose f(x) is differentiable at x=a. Then f also continuous at x=a.

A:

Q: 4. If f(x) = sin x, show that f(2.x) = 2f(x)f(-x) %3D

A:

Q: Q2 Evaluate whether the function 1-xy if xy # 1 z = x-y if xy = 1 continuous at (1,1) or not.

A:

Q: if x + 3 Q3: Let f(x) = show that f(x)is continues at x 3 %3D ifx = 3

A: Continuity Definition: A function f is said to be continuous at a point a if  fx has a definite…

Q: Let [x² + 1 _ if x 1 f(x) - Is f differentiable at 1?:

A:

Q: D etermine if continuous f(x) = X-2 x² -14 %3D at x=2

A: Here we will check that given function is continuous at x=2 ,

Q: Гa+ 4x ifx 1 Let f(x) (a) The value of a that will make f(x) continuous for all real numbers is a =…

A: Check the differentiability of a function when it is continuous at x= 1 .

Q: Q20: . Suppose that f(x) is continuous and differentiable on the interval [0,6], that f(6) = -7 and…

A: Given that the function “f (x)” is continuous and differentiable on the interval [0, 6] that, f (6)…

Q: 5) Show that the function f(x)=-÷+1 below is continuous at x = -1. x-1 2- -3 -1- -2 1.

A: A function f(x) is continuous at x=c if  We have to show that is continuous at x=-1.

Q: 34. Show that f(x) = Jã is not differentiable at x = 0.

A:

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

A:

Q: 6. Is the function given by F(x) = at x = 4? Why or why not? 1 x² - 7x + 10 continuous

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.