(a) If f is continuous and | ₁² f(x) dx = 8, show that f takes on the value 4 at least once on the interval [1,3]. (b) Approximate Question 1. That is, show that, 5 6 So S₁ 1 - dx. x 1 =dx < Xx 3 2

Q: 2. Differentiate the function f[g(x)] = = cos

A:

Q: 210 220 200 190 210 240 240 50 50 50 50 50 50 B The cross-sectional area of a marble block is given…

A: Given- The cross-sectional area of a marble block is given in the diagram above. Section lengths are…

Q: (:) X1 + 2x2 2x1 + x2 X1 + x2 Let L: R? → R³ be defined by L Let B1 and B2 be ordered bases for R?…

A: Remark: Let L : Rn -&gt; Rm be a linear transformation, then the matrix representation of L will be…

Q: Describe the interval on which the function below is continuous. X +4 f (x) = Vx %3D 10 y. 4. 21 B.…

A: topic - functions and continuity

Q: 5) Find the range of values of x for which given function is decreasing dy = 4x dx 10

A: We will find out the required value.

Q: 2. Find the intervals of increase or decrease. a) ƒ(x)=x ln x b) f(x) = xe* c) f(x) = xe¯* d) ƒ(x) =…

A:

Q: 19. (2 points) Let ƒ be an even function such that = 216 and f(x) dx = 240. Evaluate (2 - 2)5(#) dz.…

A: The given data is : ∫03fxdx=216  and  ∫-23fxdx=240 To find: ∫-22x-2fxdx…

Q: the domain of f' in interval notation Ans 7d D = f-1 e. the range off' in interval notation ans 7e…

A: f(x) = x-235inverse y = x-235interchange x and y x = y-235solve for y y = 25x2+23f-1(x) = 25x2+23

Q: 1 = x² +1 1. Use the ed definition to prove that the function f(x) = (a) continuous at x = 0. (b)…

A:

Q: 3. For which x value(s) is f(x) = sin 2x continuous? Explain why.

A:

Q: The absolute Extrema of the function f(x) = -2x – cot x on the interval -, 2] a %3D Select one: a.…

A:

Q: x + 4 6. Let f(x) find the following: x - 3 a) f(2) b) f(4) c) domain of f

A: Use the value of x for finding the function.

Q: Which among the interval whose f(x) is increasing? а. (0,5) b. (-4,0) с. (5,7) d. (-7,-4) e. None of…

A: The function y=fx is an increasing function if x increases then y also increases. that means if we…

Q: dx X1メエ16 12

A: Given integral, ∫12x2 x2+16 dx

Q: 4. Use the fplot command to plot the function f(t) lcos(3x)+ sin (4x) in the domain -25 x S2. %3D

A:

Q: IV. 4x + 2 dx x² + x + 5 V. 2x – 1 dx x² – 7x + 10 VI. | sin(3x) cos(5x) dr

A:

Q: Pleased show step-by-step

A: The given function is

Q: (a) Sketch a graph of a function f such that: f' > 0 and f" 0 and f" > 0, for x > 3. (b) Does the…

A:

Q: If f(6) = 13, f' is continuous, and f'(x) dx = 16. Find f(7) and enter a numerical value. Example,…

A: In this question given that f(6) and find the value of f(7) . We use here integration method to…

Q: csch- x dx , 0 < x < 1

A:

Q: 19.What is the derivative with respect to a of f(x) = 4-32 3z+2 4x-3

A:

Q: 21. Find 1² [f(x) + 28(x)] dx if [²₁ f(x) dx = 5_ and ₁8(1) g(x) dx = -3

A: