-1 r+1 2. If the function f(x) = I = -1 is continuous on R , then k = A -2 в -1 с о D I A B

Q: (x2 -7 , 0b Is fdifferentiable at b?

A: Given that: f(x)=x2-7,       0<x≤b6/x   ,        x>b

Q: 5- Determine the value of m such that the function z-y-4 i+ 4 VI f(r, y) = ; z+y is continuous at…

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Q: - { S 1² – 3 if r -1 2. Determine the constant k such that the function f(r) is continuous at r =…

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Q: -2 x<-1 Q1)a) For what values of a and b is g(x) = |ax – b -1 < x< 1, x 21 Continuous at x-0

A: from given function , the value of function in between 1 and -1 is ax-b. As x approaches to 0 the…

Q: x+2 x<2 1) Let f(x)={ ax² – bx+3, ; 2sx<3 x 23 2x-a+b Find the values of the constants a and b given…

A: Here I am attaching image so that you understand each and every step.

Q: 4.1 Suppose that f.g and g' are continuous on the interval Show that f(r)dg(z) exists, and…

A: Given: Assume that the variables f,g, and g'are continuous over the interval I=x:a≤x≤b Demonstrate…

Q: Which of the following is the function h(x,y) that satisfies the equation h(x, y).fxx+ X.fxy-fyy =0…

A: We will calculate all the partial derivativea and proceed

Q: z sin (), if (2, y) # (0, 0) 2. Determine if a function f : R2 → R defined by f (x, y) = %3D 0, if…

A:

Q: 5x The interval over which the function f(x)= e (1+x) becomes continuous is O [-1, 0) O (-0,…

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Q: [2sin(4) 15. Given that /(x) = k, is a continuous function at z = 0, the value of k is A O D 2

A: Solve using the limit difinition of the continuity

Q: xy³ Q3: Let f(x,y)=2x² + y² 1 (x, y) = (0,0) Is f continuous at (0,0) ? Is f continuous at every…

A:

Q: Easy Calculus question, I will rate and like! Thank you for your work!

A: We have to find

Q: If the function 2²+y? if (x, y) # (0,0) f(x, y) = 1-e(z2+y2) ? т, if (x, y) = (0,0) is continuous…

A:

Q: Which of the following is the function h(x,y) that satisfies the equation h(x,y).fx+x.fxy +yfy-0…

A:

Q: xy³ Q3: Let f(x,y)=2x²+y² 1 (x, y) = (0,0) Is f continuous at (0,0) ? Is f continuous at every point…

A:

Q: if I 2 1. Determine the constant k such that the function f(r) is continuous at I = 2.

A:

Q: 3. Find a value of b so that the function x 1 f(x) = is continuous on (-0, 0).

A: A function is said to be continuous if Left Hand limit = Right Hand limit = f(a) In this question,…

Q: The function f(x)= (x² – 1)³, is decreasing on the interval (- 00 , – 2) U (0,2) ^O (-1,0)U (1, ∞o )…

A:

Q: x² – 16 tate why f(x) is continuous on [1, 2]. x² – 9

A: f(x) is continuous on [a,b] if and only if  1. ∀x0∈(a,b)⊆R, limx→x0f(x)=f(x0) 2. limx→a+f(x)=f(a)…

Q: 7. For what value of the constants A and B is the function f continuous on (-0o, 0)E AV-x+6-1 for x…

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Q: -2? + 15z - 27 f(z) = 3z2 + 7z + 6 C, I= 3 What value of C would make f(x) continuous at z = 3?

A:

Q: x²-y² x²+y2 (x, y) = (0,0) For which value of "a" the function f (x,y) is continuous? (x, y) = (0,0)

A: Continuity.

Q: Зx2 — 1 if x 1 Determine c and d so that f is continuous everywhere

A:

Q: -2 x< -1 Q1)a) For what values of a and b is g(x) = ах — b -1<x<1, x21 Continuous at x= -1

A: The suitable formula for continious       LEFT HAND LIMIT = RIGHT HAND LIMIT

Q: 8. Find the value of a if F = (axy-z)i+(x+2 yz) j+(y - axz)k is irrotational. %3D

A:

Q: (x²-x for x +0 If f(x) : and if fis continuous at x = 0, then k= 2x f(0) = k -1/2 O 1/2 O 1

A: f(x) = (x2 - x)/2x limx→0 x2-x2xlimx→0 x(x-1)2xlimx→0 x-12= -12

Q: 1) Find the value of Z that make the function continuous at x=4? V-2 x + 4 X-4 f(x) = {z3 x = 4

A:

Q: (c) Let g : R → R be a continuous function such that +5x-9 g(t) dt = –3x . Help Willow find the…

A:

Q: 2 The function f(x) = ( x2 – 1)3 is increasing on the interval OA(-0,-2)U(0,2) OB. (-1,0) U (1, o)…

A: First, let us find the derivative of the function as shown below:…

Q: 3. (2') Let A+ cos x x 2. Given that q(x) is a continuous function, determine the value of A and B.

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Q: x³y 3. Determine if f(x,y) is continuous at (0,0). %| x6 + y2 trial paths: X = y x = y? y = x³

A:

Q: -1.5 0 1.5 For what value of constant c is the function k(x) continuous at x = 0 if k(x)= No such…

A:

Q: 25. Find the constant(s) c for which the function f(x) is continuous on (-∞,+ ∞) (c? — х2 , х<2 12…

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Q: 25. The function g(x) = [", |u| du is not differentiable at x = 0.

A:

Q: Given a function y² z f(w, x, y, z) = 2(w + 1)²x - xe² + W which of the following is not part of the…

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Q: For what value of the constant a is the function continuous on (-0, 0). for r 1 f(x) ax a =

A:

Q: -2 x<-1 Q1)a) For what values of a and b is g(x) = |ax - b - 1<x< 1, 3 x21 Continuous at x=1

A: From  the given problem:   gx=-2x≤-1ax-b-1≤x&lt;13x≥1     As we know that a function f(x) is…

Q: 1+ cx, if x 2 Given the function: f(x) = C - x, What should be the value of c so thatf is…

A:

Q: xY 10.3.5. Can the function f(x, y) be extended to a continuous function on R²? |x|+ \y]|

A: Here, the given function is: f(x,y)=xy|x|+|y| which is not continuous at (0,0). To extend it on ℝ2…

Q: -2 x<-1 Q1)a) For what values of a and b is g(x) = |ax - b -1<x<1, 3 x21 Continuous at x=0

A: F is continuous at any point then left hand limit is equal to right hand limit. if limit is not…

Q: f is a function of only x, g is a function of only y, and f and g satisfy ln(f(x)) + ln(g(y)) = ln(1…

A:

Q: [ 2 sin(;) 15. Given that f(x) =- ki, is a continuous function at z = 0, the value of k is x = 0 B !…

A: A function f(x) is continuous at x=a, if right hand limit = left hand limit = function value at x=a…

Q: The function 5· x. y g(x, y) -20 · y + 2· x + 6 is continuous everywhere on R? except on a line I in…

A: The given function is: g(x,y)=5xy-20y+2x+6...(1)

Q: Let f(x), g(x) be two continuously differentiable functions satisfying the relationships f'(x) =…

A: Introduction :

Q: 1. Find if the function is continuous in the given points (x, y) = (0,0) (x, y) = (0,0) x + y = 0 x…

A:

Q: 3x? – 1 if x 1 Determine c and d so that f is continuous everywhere (as indicated in the figure) -1

A: Given  f(x)=3x2-1if x&lt;0cx+dif 0≤x1x+8if x&gt;1

Q: 2.3.9. Which of the following functions on R2 can be defined continuously at 0? xª – y 2² – y3 g(x,…

A:

Q: Find the domain of the function f(x, y) = ln(8 – x° ? – 4y²). | - > 1} 2. {(r, v) : + 1} 4. {(x, v)…

A: We need to find the domain of the given function.

Q: 1 if z 0. Is F(x) is continuous at I = 0? Justify your answer.

A: Given that for x&lt;=0, F(x) = (x - 1)/4 Then as x tends to zero from the negative side of zero, we…

Q: Suppose f(x) is an invertible differentiable function and the graph of f passes through the points 1…

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.