The function h(x) = sin væ² + 1, x E R is continuous on: O R\{-1} O R\{-1,1} O R\{0} O R O R\{1}

Q: et fand g be continuous on the closed interval L0,5]. suppose that / s(x)dr=A, / f(x) dr =B, |…

A: we have to find

Q: (a) Can [sin (x+y)]/(x+ y) be made continuous by suitably defining it at (0, 0)? (b) Can xy/(x² +y²)…

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Q: Define g : R →R x sin (1/x), g(x) = 10, x # 0 x = 0. Explain why g is continuous at 0; in…

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Q: Determine the values of a, b, and c so that the function (sin(a + 1)x + sin x x0 is continuous for…

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Q: (b) Is the function h(u, v) = cos(u) + enu +sinh(u²)+ vv + enu , Where n=4. Is h is continuous? In…

A: (b) is the given function hu,v=cosu+enu+sinhu2+v+enu , where n=4 continuous? if yes then find the…

Q: Define f(x) = x if x is rational and f(x) = 0 if x is irrational. Compute So f dx and ſ f dx. Is f…

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Q: Let the function ƒ : R → R be given by 1- cos(x) if x + 0, f(x) := if x = 0. %3D 1 Prove that f is…

A: The solution is given as

Q: Use the limit definition of definite integral in the form of f(æ) dæ = lim {(#:)Ax, i=1 6 - a and r;…

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Q: Suppose f is integrable on [-b, b] and f is an odd function-that is, f(-t) = -f(t) for all tE(-b,…

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

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Q: Express the limit as a definite integral on the given interval. lim > n- 00 eši . Δχ [0, 8] 5 + Xi i…

A: Given: limn→∞ ∑i=1nexi5+xi∆x,   0,8. To Show: Express the limit as a definite integral on the given…

Q: Let xª sin , x + 0; f(x) ={ 0, x = 0, where a > 0 is a parameter. 1. For which values of a is f(x)…

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Q: Let f be the function defined by S1+x, when 0<x<}, }<x<1 0, when x-1. f(x)= Show that fis integrable…

A: Recall the Result/Theorem A bounded function f which has only a finite number of points of…

Q: 5. If we define the function F(s) by the improper integral F(s) = | f(x)e-" dx, %3D 0, where f(x) =…

A: Given: F(s)=∫0∞f(x) e-sx dx,f(x)=x2 We have to calculate F(s) for all s&gt;0

Q: 2. Let f(x) = { I , if r € [0, 1] 1, if r € (1, 2] Using the definition of the definite integral,…

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Q: The Fourier integrals of two continuous functions f(x) and g(x) defined on R are given by = - 2n…

A: The fourier integrals of two continuous fx and gx defined on ℝ are defined…

Q: Let f be a function on [0, 7] whose second order derivative is continuous and f(r) = 1. Suppose that…

A: We have to solve given problem:

Q: Which of the following is always true for integrable functions f and g? OSrw-dw]dx= [otwiax- frimax…

A: For integrable functions f and g

Q: 2. a) Compute the integral fa f(x) dx using 5 point composite rectangle, trapezoid and Simpson rules…

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Q: The Fourier integrals of two continuous functions f(x) and g(x) defined on R are given by sintwa] 2л…

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Q: 1. Consider the function f defined on [0, 0), f (x) = {x* sin- x + 0 x = 0 where r > 0. Determine…

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Q: Discuss whether the following functions are continuous at the specified point(s). sin(x) (a) f(x) =…

A: To determine whether the following functions are continuous at the specified points or not. (a)…

Q: Define h(x) = x³ sin(1/x) for x + 0 and h(0) = 0. Prove that h' is not differentiable at x = 0. .

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Q: Find the Wronskian for the set of functions.{x, ex, sin x, cos x}

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Q: 1. Consider the function f:R → R: S(z) = sin(2) Determine if this function is: (a) differentiable…

A: Given that fx=sinxx To determine the function is (a) differentiable (b) locally Lipschitz continuous…

Q: has a limit at xo + 0. If Q2. Let f:R → R be a function such that f(x) x sin f is defined at xo,…

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

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Q: 1. Consider the function Sa(1 – x) sin r€ (0, 1), πε (0, 1) , - f (x) = %3D (0, x € {0, 1}. (a)…

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Q: Let f(x, y) = Scosy.sinx, x # 0 cosy, x = 0 Is f continuous at (0,0)? Is ƒ continuous everywhere?

A: We have to check whether the given function is continuous at x = 0 or not. Also, check whether it is…

Q: 3. Define f:R –→ R by ƒ (x) = sin (1/x) if x # 0 and f (0) = 0. (a) Show that fis not continuous at…

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

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Q: Q2. Let f:R→ R be a function such that f(x) = x sin (-) has a limit at xo + 0. If f is defined at xo…

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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: The limit n lim E /2x + (x; )²Ax i=1 can be expressed as a definite integral on the interval [1, 8]…

A: Concept used: Definition of definite integral is given by ∫abf(x)dx=limn→∞∑i=1nf(xi)△x…

Q: Consider ſ, (x² – 9)dx. Use the definition of the definite integral to evaluate this integral as the…

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Q: The limit n lim E V2x; + (x; )²Ax can be expressed as a definite integral on the interval [1, 8] of…

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Q: Find the function f(a) such that f'(x) = 5 sinh(x) – 2 and f(0) = 4. a) O f(x) =-5 cosh(x) – 2 z - 1…

A: Given that f'(x)=5sinh(x)-2 and f(0)=4 To find the function f(x)

Q: Let f be the function defined by SI+x, when 0<x<!, }<x<1 0, when x=1. f(x)=: Show that fis…

A: We know that  A bounded function f which has only a finite number of points of discontinuity in…

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

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Q: ind the absolute maximum and minimum values of f on the given interval. a) f(x) = on [0, 2] g2+1 on…

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

A: We need to evaluate integral.

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

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Q: The limit lim e 1+i i=1 n00 can be expressed as a definite integral on the interval [1, 5] of the…

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Q: 3. Evaluate the limit r(t +h) - r(t) lim h→0 h for r(t) = (t-1, sin(t), 4).

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Q: a non zero valie for the constant k that makes the fmction ww m tan(kx) x< 0 f(x) = 3x + 2k?, x 20…

A: To find a non zero value for the constant k that makes the function…

Q: a) f is continuous on [0,∞] b) f is differentiable on [0,∞) c) f' exists and is differentiable on…

A: Given: The function is  f(x) =xr sin1x ,         x≠00,                     x=0

Q: Determine where h(x) = sin(x- Sx + 2) is continuous. %3D h is continuous on the interval [0, co). h…

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Q: ) Let f(x) = cos(x) ln (1+ ax 1+bx, 1 1 2'2 If f(x)dx = 0 where a and b are real be integrable on…

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