Find the value of r*d(\x[³).

Q: Use the Mean Value Theorem to establish e > 1+ x, x > 0. Answer:

A:

Q: Let f(e) = In[r*(z + 6}*(z° + 6)"] f'(x) =

A: Given: Now,         f'(x)=lnx4x+62x2+69'        =1x4x+62x2+69x4x+62x2+69'…

Q: Consider the function f(x) = 2x10 + 7x° – 6x² – 9. Enter the antiderivative of f(x) -

A: To find The anti derivative of f(x).

Q: Explain why the Intermediate Value Theorem is not necess arily guaranteed fo f (x) = = CSC for x E…

A: Topic = Functions   The intermediate value theorem states that if f is a continuous function whose…

Q: If f is continuous and f(x) dx = 8, find xf(x?) dx. %3D

A:

Q: For what value of c is the function defined below continuous on (-o, o)? – c², f(x) = { x - c², x<…

A:

Q: Please show step-by-step solution

A:

Q: c. Use antidifferentiation to find f (x).

A: Since, we have asked for solving part-(c) only.Since here it is given that f'(x)=x2 ln x -(i)Here…

Q: Fundamental Theorem of Calculus.

A: ∫abfx dx

Q: f(x)=210, where is it continuous?

A: Given: fx=210 We know that graph of given function is horizontal line for every value of x

Q: For what values of a is Jaʼx – 2a, x2 2 f(x) ( 12, x< 2 continuous at every x?

A: Given : The function is f(x) =a2x - 2a        , x ≥212,                     x&lt;2 .

Q: Let f be a continuous function such that -6 [', f(x) dx = 9. What is the value of -3 f(x) dx = -10…

A:

Q: Find, if they exist, the extrema of the function: f(x, y) = x² + 3y? + 4,

A:

Q: 2 Evaluate f(x) dx, given that f(x) dx = 6.

A: ∫abf(x)dx=-∫baf(x) dx

Q: For what values of a is

A:

Q: For what values of a and b is -2, f(x) = { ax – b, -1 <x< 1 3, continuous at every x?

A: Given: fx=-2,    x≤-1ax-b,    -1&lt;x&lt;13,   x≥1

Q: Where is the function f(r, y) = x/y continuous?

A:

Q: Based on your work in part a, on what interval(s) is f(x) continuous?

A:

Q: If f is continuous and f(x) dx = 2, find xf(x²) dx. Need Help? Read It

A: We Definite integral properties by using substitution method

Q: State the interval(s) over which the function f(x) = V16 – x² is continuous.

A: Given, fx = 16-x2   We have to state the interval over which the function is continuous.

Q: For what value of b is

A:

Q: Find the values of a and b that make f continuous everywhere.

A:

Q: Determine the set of x-values where y = x - 4 r2 +9r+18 is continuous, using interval notation.

A:

Q: For what values of a is Ja'x – 2a, x 2 2 f(x) : \ 12, x < 2 continuous at every x?

A: Given function is Since f(x) is continuous for every x. So, f(x) is continuous at x=2.

Q: For what value of a is

A: Given           f(x)=x2-1    ,  x&lt;32ax       ,   x≥3

Q: Use the intermediate value theorem to find the value of c such that f(c) = M. c =

A:

Q: ff is continuous and f(x) dx = 19, evaluate f(2x) dx.

A: Given that a integration and we solve use these integration to another integral value.     Here i…

Q: Let f be a continuous function such that | f(x) dæ = 5 and f(x) dx = 3. %3D | 4f(æ) dæ? What is the…

A: Recall: Properties of integral:  i)   ∫abf(x)dx=-∫baf(x)dxii) ∫abf(x)dx+∫bcf(x)dx=∫acf(x)dxiii)…

Q: Use tabular method to evaluate f a*e¬k« dx

A: We need to use the integration by parts:∫uvdx=u∫vdx-∫u'∫vdxdx

Q: Define what it means by for y f(x) dx

A:

Q: Use the definition to show that the function f(x) = → is continuous on the interval [c, o), %3D…

A: The given function is f(x)=1x2 .we have to show that f(x) is continuous on the intervel [c,∞)…

Q: On what domain is the function f(x) = – 4+ v–48 – 6x continuous?

A: The given function is: f(x)=-4+-48-6x

Q: Find the average vale ot f(x)=Dx²e-2x overthe interval [-1,1]

A:

Q: Find the particular sölution f"(x) = 4, f'(2) = 12, f(2) = 17

A: integration 2 times and after applying initial condition we get f(x)

Q: For f(z) =, find dy using the definition, 127

A:

Q: f(x)=sqrt(x)e^(x)+x find the derrivative.

A:

Q: Where is f(a) not continuous?

A: Given:

Q: Q3) For what values of a and b are -х2 +а , x<0 x in+1, 0 < x<- y = bx3 + 2, Continuous at every x ?

A:

Q: Find the value of c such that

A: Given∑n=0∞enc=7

Q: f is continuous and f(x) dx = 8, find xfc

A: we have to find

Q: Approximate V126 using Ay f'(x) · Ax

A: Given,  126

Q: Q3) For what values of a and b are (-x² + a , y = { xsin-+1, 0 < xs: bx³ + 2 , Continuous at every x…

A: See the attachment

Q: What is the antiderative of xysin((x^2)y)?

A:

Q: If f is continuous and f(x)dx = 4, find So xf (x?)dx. %3D

A:

Q: de fined as F(X) = P(X f(t) for – a <x < a. - t<a

A: Here f(t) is probability density function of x.  Where -a&lt;x&lt;a.

Q: Let f be a continuous function such that f (x) dx = -4 and 1 f(x) dx = –14. What is the value of 2…

A: As we know that;  The properties of the definite integral; 1). ∫abfxdx=-∫bafxdx…

Q: Q3) For what values of a and b are ax + 2b , y = x2 + 3a -b, 3x-5, 0 2 Continuous at every x ?

A: We will check continuity at breaking points of the function. For continuity , left hand limit and…

Q: Q3) For what values of a and b are (-x² +a, y ={ xsin - bx3 + 2 , 0 <x<: Continuous at every x ?

A: Given information: The function is y=x2+a          x≤0xsin1x+1   0&lt;x≤1πbx3+2       x&gt;1π…

Q: The solut (Туре yoL

A: This is a question on inequality from graph

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.