37. Which one of the following real functions is continuous on R ? A Inr 2 +1 I+1 D tanz

Q: if f is continuous on R, prove that. integral a to b (f(-x)) dx= integral -b to -a f(x) dx.  for…

A: f is continuous on R,∫abf-xdx = ∫-b-afxdxwhere fx>0 and 0≤a<b

Q: State TRUE or FALSE giving proper justification for the following statement. There exists a…

A: The given statement is : "There exists a continuous function f:ℝ→ℝ2 such that f(cosn)=(n,1n) for all…

Q: Let fand g be continuous on the closed interval l0.5]. suppose S'(1) dr=4, ] s(x)dr=B, s(x)dx=C. The…

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Q: Let f and g be continuous on the closed interval (0, 5). Suppose that f(x)dx = A, f(x)dx =B, and…

A:

Q: For what value of b is

A: The given function is continuous for all x<0 and for all x>0, because it is a polynomial…

Q: 2. Which of the following is continuous at x = 0? I. g(x) = |x| II. g(x) = e* III. g(x) = In(e* – 1)…

A: For the function, fx to be continuous at x=a: limx→af(x)=f(a)

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?…

A: Given: Function f(x) = 3x - cosx  To Find The x - values for which the given function is not…

Q: 45. For what value of a is Jx? - 1, x< 3 | 2ax, f(x) x2 3 continuous at every x?

A: Given: fx=x2-1,x&lt;32ax,x≥3 We know that given function will be continuous at every value of x, if…

Q: Let fand g be continuous on the closed interval [0.5]. suppose that f(x)dx=A, 8(x)dr=C. The 5…

A: We can evaluate the given integral by using the following properties

Q: Q3) For what values of a and b are ax + 2b , y = x? + 3a -b, 3x-5, x 2 Continuous at every x ?

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Q: Suppose f is an odd continuous function whose mean value (with respect to integral) on the interval…

A:

Q: Determine whether the statement is true or false. f(t) : e-t- et 2 is continuous everywhere. O True…

A: Given that f(t)=2e-t-et Now, e-t-et =0 gives1et=etor, 1=e2tor, et=1or, t=0

Q: Suppose f is continuous on the closed interval [–1, 3). If F is an antiderivative of f, which of the…

A:

Q: 10, Let f be the function defined by the following. sin x, x<0 x. Osx<1 S(x)={ 2-x, x-3, x22 For…

A: Given: the function f defined by the following             fx=sin…

Q: 46. Find the values of a and b that make ƒ continuous everywhere. 4 - if x < 2 f(x) = ax? if 2 <x <…

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Q: . Show wheth er the following function is continuous at x = 0.

A: Givenf(x)=4x-9 if x&gt;-33x+6 if x≤-3

Q: Suppose f is an odd continuous function whose mean value (with respect to integral) on the interval…

A:

Q: Which of the following functions is continuous at x = 0? S x+1 if x 0 b. sin(x) if x 0 Ос O c.…

A:

Q: Suppose f is an odd continuous function whose mean value (with respect to integral) on the interval…

A:

Q: For what values of a is Ja'x – 2a, x 2 2 f(x) : \ 12, x < 2 continuous at every x?

A: Given function is Since f(x) is continuous for every x. So, f(x) is continuous at x=2.

Q: Let f and g be continuous on the closed interval [0,5]. Suppose that Į f(x)dr=A, f(x)dr=B, integral…

A: we have to find

Q: 1 Express the following functions in the form utiv • f(Z) = ln (1+z)

A: This is a problem related to complex number. Please follow the procedure given below.

Q: 10. Which of the following functions is differentiable for every x ? O a) f(x) = |x| O b) f(x) =…

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

Q: 3 Let fand g be continuous on the closed interval [0,5]. suppose that / f(x)dx=A, / f(x)dx =B,…

A:

Q: Suppose f is continuous on the closed interval [–1, 3]. If F is an antiderivative of f, which of the…

A: Let's find.

Q: a) For which values of a and b in R is f(x) continuous on (-infinity, pi/2)? b) For which values of…

A: Given function is f(x)=x+a, x≤0bcos(x)+asin(x) , 0&lt;x≤π4btan(x), x≥π4 If f(x) is continuous on…

Q: roblem 4 At what points of R² are the following functions continuous? 1. f(x,y) = =²–-y? 2xy

A: To determine the continuity of the following function

Q: 37. Which one of the following real functions is continuous on R? A Inr B 2 +1 I+I tanz C r+1 D

A: Given: A. ln(x) B. xx2+1 C. x+1 D tan (x)

Q: Consider the function f that is continuous on the interval [-5, 5] and for which 5 f(x)dx = 4.…

A:

Q: Let fand g be continuous on the closed interval L0.5] Suppose that f(x)dr=/ 8(x) dr=C_ The definite…

A: Given that: ∫05f(x) dx=A,∫03f(x) dx=B,∫53g(x) dx=C We have to find the definite integral…

Q: Which of the following interval is f(x) = O (2, +∞0) O [2, +∞0) 0 (-∞0, +∞0) ○ (0, +∞) 1 Vx…

A:

Q: Which of the following functions is continuous at (0, 0 )? f( x, y ) = In ( x² + y² ) ху Оb.f (x, у…

A: Which function is continue at point x and y=0

Q: 26. Assume that f is continuous and f(x) dx = 12. Find %3D f(x³)x² dx

A:

Q: x = 0 f(x) sin z x +0 а) х — 0. ? b) х — 4т. ?

A:

Q: Which of the following functions will be continuous on (0, 3)? OA. h() = 12 8² + 6| OB. g() = 7/2-16…

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Q: Consider the function f that is continuous on the interval [-8, 8] and for which the following is…

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Q: Q3) For what values of a and b are ax + 2b , y = {x? + 3a -b, (3x-5 , 0 2 Continuous at every x ?

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Q: B/ For what value of a is fo continuous at every x? x? – 1, x< 3 { fx) = 2ах, x2 3

A: Our objective is to find the value of a for which f(x) is continuous at every x.

Q: Is the function h(u, v) = cos(u) + emu +sinh(u?)+ vv + emu , Where n=6. Is h is continuous? In case…

A:

Q: Let fand g be continuous on the closed interval [0,5]. suppose that / f(x)dr=A, / f(x) dr =B, |…

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Q: 10. Let L : R² → R be given by 2²–y? if x + y # 0 L(x) = L(x, y) = I+y 2x otherwise Decide whether L…

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Q: 26. Which one of the following functions is bounded in R? cosh r sinh r C tanh r D

A: Real functions are given , we have to find the bounded function

Q: Suppose f is continuous on the closed interval [–1,3]. If F is an antiderivative of f, which of the…

A:

Q: Which of the following functions are continuous on the entire interval (1,9)? Circle all that oly.…

A: Given function is  fx=e3x-42x-7 Clearly f(x) is defined everywhere except at x=72 and 72∈1,9 So,…

Q: Let fand g be continuous on the closed interval [0,5]. Suppose that / f (x) dr =A, / f(x)dx=B, 8(:…

A:

Q: 19. If f is continuous and o f(x) dr = 20, find | #f(x*) dx af(r²)dr

A: given ∫09f(x)dx=20  and we need to find ∫09xf(x2)dx=?

Q: ind the values of a and b to make the function f(x) is continuous everywhere sin ax if x <0 f(x) = {…

A: Given function is f(x)=sinaxx, x&lt;0x-1x2-1+b , 0≤x&lt;1x+1, x≥1…

Q: Suppose f is an odd continuous function whose mean value (with respect to integral) on the interval…

A:

Q: Let ƒ and g be continuous on the closed interval [0, 5]. Suppose that | f(x)dx = A, | f(#)dr = B ,a…

A: Given that: ∫05f(x)dx=A, ∫03f(x)dx=B and ∫53g(x)dx=C

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.