(4) Suppose f(x) is increasing on [a,b]. Let P₁ = {xo, ₁,...,n}, where xk = a + k (b − a), k = 0, 1,..., n. Prove that and [ f(x) dx 0 ≤ U(³Pm S) - fº f(x) dx ≤ b=ª (ƒ(1) — S (a)) n = lim U(Pn, f). 8个

Q: The integer n = 12700140x3243243 is missing the digit x. a) If n congruent to  3 (mod 9), then what…

A: According to the given information, Consider the given integer n:

Q: If h and f are functions and g defined by g(t) = f(t) · h(t), then what is g'(t)? f'(t)h'(t) +…

A: We have given that gt=ft·ht Differentiate the above function w.r.t 't' g't=ddtft·ht

Q: If f(x) is continuous on (-15,-5)such that, -10 SI5 f(x)dx=13 and/" f(x)dx =6 then find f(x)dx -10…

A:

Q: 1) Consider the function f(x): = 5x² - 4x +7 Find a number c in the domain such that f (c) = defined…

A: Given: fx=5x2-4x+7 for x∈1, 4 To be find c∈1, 4 such that fc=13∫14fxdx Integral of ∫xndx is given by…

Q: Consider the function f(x) = e (x² + 1). (a) Given that f'(x) = e² (x² + 2x + 1), determine the…

A: Solution is given below:

Q: Calculate Rs for f(x) = 6 - x over ver [3,5]. R8 IE

A:

Q: Maximise the function f(x, y) = 4xy² subject to r + y? = 2.

A:

Q: Suppose that f'(t)-29 (b)31 (e)none of these

A: Given: Suppose that f'(t)<3 for all t in R and f(3)=1. To find: f(-7)  Lagrange’s mean value…

Q: What is T₂(x) centered at a = 3 for a function f(x) such that f(3) = 9, f '(3) = 8, f "(3) = 4, and…

A:

Q: 6. Does there exist a continuous function on the interval [0, 2] such that f(0) = 0, f(2) = 7, and…

A:

Q: 4. Find f"(2). (a) f(u) = 2u²5 – u).

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Q: 6. Let S = {-1,0, 2, 4, 7}. Find f(S) (image of S under f) where f is from R to R for (a) f(a) = 1…

A: The

Q: Evaluate f(1) dz, where S7a, 0<<1 f(z) = 4x2, 1<< 2. f(z) dr =

A:

Q: Let f(x) - x|x|. (a) Sketch the graph of the function. y 2 -2 -2 -2 -2- -2 -2 -4 -4 -4 (b) For what…

A: Objective is to find the function and check the differerentiability.

Q: 6. Let f be a function such that f(2) = 3 and f(6) = 19. Which of the following conditions…

A:

Q: 2. a) Give an example of a function f: R →R that is differentiable everywhere and 1- to-1, but f'(x)…

A: Let, f(x) = x3 .      Then, f(x), being a polynomial, is differentiable for all x ∈ R, i.e.,…

Q: 5. If X any Y are sets, then X-Y= {r€ X: 1¢Y} If X is open set and Y is closed set. Prove that (a)…

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Q: 2 Iƒ ƒn(x) = efn−1(x) for all ne N and fo If d nd {ƒn(x)}. dx

A:

Q: Anna is to create a garden plot to grow lettuce (area A) for her turtles, as well as flowers (area…

A: When the given curve y = 9 - x2 intersects the x-axis, we have                y = 9 - x2 = 0…

Q: Let F(s)= [f(x-s)d. Find F(s) for the function f(x)= x", where n is a constant.

A: The power rule for integration is ∫x5dx=x66+C. Here, C is the constant and x is the integration…

Q: If f is a positive function and f"(x) < 0 for a < xs b, show that T, < f(x) dx < M,

A: f is a positive function and f''(x)&lt;0 for a≤x≤b This tells us that f is concave down over the…

Q: 1. Use the definition to find f'(e) if it exists *, if z< 3 S(x) = c= 3 -3r, if r 23

A:

Q: 20. The function f is continuous at x = 1. Vx + 3 -. - V3x + 1 for x 1 x - 1 If f(x) = k for x = 1…

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Q: .     f(x) = a/x2+b2 B.      f(x) = sin(ax+b) C.     f(x) = (x-a)(x-b) describe the critical…

A: Solving questions

Q: Calculate M6 for f(x) = 5 · In(æ³) over [1, 2].

A: Given:   f(x)=5.ln(x3) over [1,3]