dx Show that f - In|ax + b| + C where a # 0. ax+b

Q: 13. If f(x) = 1 / (5 + 7x) , find S f(x) by using a u-substitution. Show the u-substitutions.

A: Given, fx = 15 +7x  We have to find ∫fx using u substitution

Q: (c) Suppose that ƒ hits every value between y = 0 and y = 1 on the interval [0, 1]. Must ƒ be…

A: A function is continuous when its graph is a single unbroken curve , that you could draw without…

Q: 4. (5pt) If f(r) = [t – 1) cosh t dt, on what interval is ƒ increasing? (Hint: Use the Fundamental…

A:

Q: he Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 5+x2 Ciuo Hooim

A: Here we have to use linear approximation rule.

Q: b) Let f be a differentiable function of one variable, and let z = f(3x² – 5y²). Show that az əz…

A: Given  z = 3x2 - 5y2

Q: 21. f(x) = In (5-3x²)' J6x² + 21. f(x)= In| (5-3x V6x? + 8х —12 1+5t 22. f(t)= In(t)

A: As per our guidelines, I can answer maximum one question. Since you have asked for multiple…

Q: 6. Use an appropriate substitution to prove f(r)dr = f(a + b – x)dr. %3D

A: We have to prove definite integral property.

Q: 3. Find f(x) if f'(x) = sec²x - sinx and f(TT/4) = 1. %3D %3D

A: Given: f'(x) = sec2x -sinx  To find: The value of f(x)  and  fπ4.

Q: Ex/l let fi [1₂1]-> R be function f(x) = 3 x70 2 x < 0 Is the function integrable and Continuous?

A:

Q: Let f(z) - 4z-1 pnd alz) - ar+b, where a pnd b are positive constants. If the composite

A:

Q: Q3-A) Is the function F(Z) continuous or not at z-U? 1+|21,

A: Let z = x+iy then Re(z) = x and |z| = √(x^2 + y^2) If z = 0 =&gt; x = 0 and y = 0

Q: 2. f(x) = Vx – 1 at x = 5

A: Function is continuous and differentiable both at x= 5.....for detail...go through the solution

Q: Give an example where | f(x)dg(x) exist even through f is unbounded on [a, b].

A:

Q: 5. Use the Second Fundamental Theorem of Calculus to find F'(x). х 1 F(x) = S* dt.

A:

Q: Find the extreme values of f(r) = Vr(5 – x) in the interval [–1,3].

A: For extreme points we need to find critical points and check value of f(x) on boundary values of…

Q: Suppose that f(x, y) = yvx* + 1 on the domain D = {(x, y) | 0 < y < x < 5}.

A:

Q: 6. Use an appropriate substitution to prove f(x)dr = | f(a+b- x)dx.

A: To use an appropriate substitute to prove  ∫abfxdx=∫abfa+b-xdx

Q: Show that if f (x, y, z) = 0 then = -1.

A:

Q: Use the Linear Approximation to estimate Af = f(4.8) – f(5) for f(x) = x – 5x². (Use decimal…

A: Given data:   The given expression for the function is f(x)=x-5x2. The given value a=5.   The…

Q: Let f(æ) = – 3x* In æ %3D f'(x) = f'(e²) =

A:

Q: Let F (x) = %3D In tdt then F' (x) = et3

A: To find F'(t)

Q: Use the function f(x) = Vx and a starting point of a = 8 with linear approx- imation to approximate…

A:

Q: Suppose that f (1) = 2 ,f (4) =7, f '(1) = 5, f '(4) = 3and f" is continuous. Find the value of ∫1…

A: Given f1=2f4=7f'1=5f'4=3 f''x is continuous To find value of ∫14xf''xdx

Q: Left- and right-continuity a. Is hlx2 = Vx - 9 left-continuous at x = 3? Explain. b. Is h1x2 = Vx -…

A: To Determine: find left hand and right hand continuity at x=3 and explain this Given: we have a…

Q: Describe the long run behavior of f(x) = x* As x → ∞, f(x) → ? As x → 0, f(x) → ?

A: This question is about function behaviour near infinity

Q: Let F (x) = *e3x %3D In tdt then F' (x) = et3 %3D

A: Tp evaluate the given definite integral and to find the derivative of F(x)

Q: Q2 Let f(x) = c x= 0,1,2,3, . 1-find c ? 2-find EX(X – 1) ?

A: Given a probability mass function; f(x)=c2xx!, x=0, 1, 2, 3, ... 1. We know that a very important…

Q: Coo show that the f(x,y)=X+4xy-3y gdegrad is homogenaow of

A: Concept used: The function is homogeneous of degree n if fkx,ky=knfx,y. Given: fx,y=x3+xy2-3y3…

Q: Describe the long run behavior of f(2) = - z As z + - 00, f(z) + ? As a + 00, f(æ) → ?

A:

Q: ) Differentiate f(r) = In(v²) + In(10). Hint: Think before differentiate :) you

A:

Q: If f(x) = 2sin-'(u) where u =L, then: f'(x) = %3D f (2) =

A:

Q: 9. If f is continuous and f(3x) dx. f(x) dx = 8, evaluate Answer:

A: Given:

Q: Where is f(a) not continuous?

A: Given:

Q: Let f(x) = ax* + bx . If (1,6) is a relative extremum point, then b is?

A:

Q: Let f: A→ B, where A= {1,-1}, B= {1,2,3}, and f(x)= 3×x²+2, find Range إجابتك * Codomain إجابك * Is…

A:

Q: Suppose f(r) = (In z)e. What is f'(x)?

A: d/dx (f(x)g(x))= f(x)g'(x)+g(x)f'(x)

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

A: See the attachment

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

A:

Q: Suppose f(x) = 4nx?e-Tx -e-n for all x € R. Show that f = -f. %3D

A:

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: If f is increasing on the interval [a, b), then f' does exist. Select one: a. True b. False

A: Let f is increasing on the interval [a, b]. Since, there is not given that the function is…

Q: Suppose f is a bounded real function on [a, b), and f' eR on [a, b). Does it follow that fe R? Does…

A:

Q: O Show that the function f: N2 N defined by f(x, y) = 2X3Y is injective but not surjective.

A:

Q: Let –1, -T<¤ < 0, 0, 0 < x < T. f(x) = * = 0 1,

A:

Q: 26) The interval where f(x) is decreasing is?

A: Answer and explanation is given below...

Q: Find the absolute extrema of f on [-2, 3] if f(x) = x² - 6x - 1 O √5 O 2

A:

Q: 5. Is the function given by g(x) = 4x³. 6x continuous on R?

A:

Q: Q3) For what values of a and b are -x² + a , x Continuous at every x ?

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.