29 - For uhat values of a and b is ax+2b x+3a- b くXS2 3X-5 Continuous at every X ?

Q: 3. Find and sketch the domain of f(x, y) = In(9 – x² – 9y²). [Hint: In(x), x > 0]

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Q: 3 If f(x) = 2 + x, evaluate Σƒ (k+1). atas (k k=1

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Q: Suppose f(x) = - 2x - cosr. (a) Show that f is strictly decreasing on R. (b) Hence, justify that 2x…

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Q: Find the values of a and b that make f continuous everywhere. f(x) =    (x2 − 4)/x-2        if x < 2…

A: Given fx= x2-4x-2 if x&lt;2ax2-bx+1   if 2≤x&lt;34x-a+b      if x≥3Here f is continuous everywhere…

Q: Evaluate (x by Simpson's rule breaking it into 6 intervals. 1 2+x2

A: THE EXPLANATION HAS BEEN GIVEN IN THE ATTACHED FILE.

Q: 4. Use limits to determine the values of a and b that guarantee the function below is continuous.…

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Q: 4 ,5 Let f(x) = 7x* In(x) f'(x)

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Q: 9) State the intervals of increasing and decreasing behavior in the function k(x) = x2 In x?.

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Q: 8. Is the set of functions f₁(x) = 3e³x and f₂(x) = -3e3³* independent? Show using the -3.x…

A: Given functions- f1x=3e3x  and  f2x=-3e-3x To show whether the given set of functions is independent…

Q: _25. Determine if f (x) = {"" (2x – 1 if x 5 is continuous on [2,5]. A. discontinuous on an…

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Q: II. Determine if Vx2 – 3x – 4, if x 1. is continuous or not at x = -1 and at x = 1. In the case of…

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Q: Suppose f is continuous on [1,5] and the only solutions ofthe equation  f(x)  = 6 are x = 1and x= 4…

A: Given: The function f is continuous on 1,5 and fx=6 has only two solution x=1, x=4 and f2=8, To…

Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x +1 on [-1,3]

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Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x + 1 on [-1,3]

A: Verify Rolle's theorem

Q: If Зх — 2,х <3 -{ - h(x) х4 — 74, х 2 3 Is h(x) continuous at (x=3)? 1 Add file

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Q: For what values of a, m and b does the function x = 0 0 < x < 1 1< x< 2 3, f(x) = -x² +3x + a, тх +…

A: to find the values

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

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Q: 21. Discuss the continuity of: for for 0sx 2

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Q: if ニ if 1-X fCx +2) = f(x) Hx f on [-3,3] and we Suppose draw the funch'on

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Q: 4cos20 + 2/3 = 0 on the interval[0, 3t]

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

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Q: Let f be given by x² – 4 if x 3 - 2х — а +b Determine the values of a and b that make ƒ continuous…

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Q: Let fé)--을(t)6. Eveluate f(-8) %3D f68)= ? %31

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Q: Q1) check the continuity of fX) at X- -1, 0,1.23 -1<x<1 2x-1, 3x-2 25x53 2, x=3

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Q: (b). Find the bound for absolute error at x = 2.9 on the interval [x, x,], where x, = 2.25, x, =…

A: On the interval x0,xn where x0=2.25, x1=2.5, x2=2.75, x3=3 with n=3 along with the function…

Q: Q 4. (a). Show that limit *1, does not exist if (5-4x S(x)=. -)- {ax-2 for x <1] for xz1]

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Q: (х — т 11- тх if x < 3 if x 2 3 5) Find m so that g(x) = Is continuous for all x?

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Q: 3x if xS -2 If s(x) - x -1 if -2<x<2 if x2 2 Discuss continuity at x = 2 and x =-2 3.

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Q: 3. Show that f(2) = (z+ 1)³ – 3z is nowhere analytic.

A: The given function is, fz=z+13-3z The function z is given by, z=x-iy Substitute values in above…

Q: Show whether f(x) is continuous (3х-2 f(x)={ x-2 x² -4 for x=- for x+ -

A: Given that, f(x) = 3x - 2; for x = - 2 f(x) = (x + 2)/(x^2 - 4); for x not equal to - 2 So when x is…

Q: 8 — х — x2 if x 4 -

A: f(4-) = 8 - 4 - 16 = -12 f(4+) = 2*4 - 20 = -12 f(4) = 8 - 20 = -12

Q: 7. Where is f(x.y)= continuous? Do not just write an answer, show your work or give any necessary…

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Q: 4. Verify Rolle's Theorem for f(x) = x² - 2x +1 on [-1,3]

A: Given the function f(x)=x2−2x+1 On the interval [−1,3]

Q: 6 Evaluate f S Suh

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Q: Verify mean value theorem for ƒ(x)=x' – 5x+6 over the interval [1,3].

A: Please refer to the image below

Q: 21. Discuss the continuity of : 1 x + for x 2

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Q: 6. Let f(x) = V2x + 1, find as Ax - Ax

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Q: 13,4) f(x.y) =In(x + x² +y² If Find x

A: f(x,y) = ln (x+x2+y2)∂f∂x=∂ ln (x+x2+y2)∂x=1 (x+x2+y2)×(1+12x2+y2)×2x

Q: 9. If f(x) = ], ( 22 - 5t-3 ]dt, on what interval(s) 0, is f increasing, decreasing

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Q: would you please write this part in handwriting? because im not sure i understand. Let…

A: Solution

Q: 3 Prove that Var(aX– b) = a² Var(X) where a and b are constants. %3D |

A: We know that the V(X) =E(X2) -(E(X))2 By using the  above definition of V(X), we can easily prove…

Q: (a). Find the values of a and b that make f continuous everywhere. x² -4 if x<2 x-2 f(x)={ax² - bx+3…

A: f(x)=x2-4x-2if x&lt;2ax2-bx+3if 2≤x&lt;32x- a+bif x≥3 Definition: Continuous functionLet f(x) be a…

Q: Show that f (r) = x³ – 3x2 + 2 is monotonically increasing on every interval.

A: Given that: f(x)=x3-3x2+2

Q: Q. 1: Determine the func- tion is continuous or dis- continuous at x = -1 and x = 1.

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Q: 5) Find m so that g(x) (x - m =1-mx if x <3 if x 2 3 Is continuous for all x?

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Q: 3. Show that 5 x + 7 is a continuous fimction

A: Let, f(x) = 5x+7 be defined over R, the set of all real numbers. Choose an arbitrary point c in R.…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.