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

Q: Q5: a- Use two segment trapezoidal rule to integrate the following function numerically: f(x) =…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Show that the function f(x) = e¯*/2 has inflection points x = f1. at

A: We have the given function as fx=e-x22              ⋯⋯1 As we know that, a point of inflection of…

Q: Verify Rolle's theorem for f(x) = x* – 4x+8 over the interval [0, 2].

A:

Q: 2.if f (x) = x2 + 3, with domain R then f(x) has f(x) %3D O T F

A: Here the given function is f(x)= x2+3 with domain R We need to find it has inverse or not.

Q: 3 Let f(x) = 2 + In(bx), where b is a positive constant. Find f'(x).

A:

Q: what is the quadratic polynomial for the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1)

A:

Q: on f(x, y) = 3x + 9y subject to th %3D

A:

Q: Prove that for all a, b = R, the function f(x) = 3x² - 4x³ + 6x² + ax + b has exactly one point…

A:

Q: c) lim,→1+ f(x) where f(x) = { V1- x, x 1 | x +1,

A: Given query is to find indicated limits.

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

A:

Q: 25 If f is continuous and f(x) dx = 8, find xf(x²) dx.

A: given ∫025f(x)dx=8∫05xf(x2)dx=?

Q: Find values at x where the fuction is NOT differentiable(in any) f(x)= lx-2l +3

A: Given function is By definition, we have Therefore,

Q: Find value a  such that f(x)={x^2+2x-1 if x not equal to 1…

A: given,f(x)=x2+2x-1  if  x≠1a                if x=1left hand limit at x=1limx→1- f(x)=limx→1-…

Q: B) Show that fx) = sin for x * 0. for x= 0. X = is not continuous.

A:

Q: Q2/Show that the functions is harmonic u = 2 x (1 - y)

A:

Q: Find the absolution extrema of f(x) = (In x)2 on [1, e].

A: We have to determine absolute extrema of girls question

Q: 2 If f is continuous and f(x) dx = 14, find | xf(x?) dx.

A:

Q: What is the minimum f(x) value of f(x) = sin x on the interval [0, 2]? %3!

A: Derivative Test: find values of x for which f'(x)=0 Then find f''(x) and put values pf x from above…

Q: 1. Suppose that f f(x) dx = In x + Vx+1+C. Can f be a rational function? Explain.

A: To explain f is a rational function or not.

Q: Find all antiderivatives of function:  f (x) = -4x

A: An antiderivative of a function f(x) is the indefinite integral ∫f(x)dx. Denote this antiderivative…

Q: 2) An elastic tire is described by the iven by the function f(x, y) = 4xy. Use

A: Introduction: The Lagrange methodology is employed to maximize or minimize a general performance…

Q: Suppose that f and g are discontinuous at x = c. Does it follow that f + g is discontinuous at x =…

A: Let us define that Then both f and g are discontinuous at x=2

Q: -Q3/As the function f(x,y) = at (-1,2) xy 1 + x² + y² is Continuous

A: Here we have to check the continuity of the function at the given point.

Q: 66. What will be the function g(x) resulting from normalizing the function f(x) = x³ − x4 defined in…

A: To find : function gx resulting from normalizing the function fx=x3-x4 defined in the domain 0, 34

Q: 8. If f is continuous and f(x) dx = 12, find f(2x) dx. 0.

A: Given f is continuous and ∫08f(x)dx=12

Q: 14. Consider the function f (x) = x²e+x . f(x) has two inflection points at x = _ and x =_.

A:

Q: Q5: Differentiate the following: a. f(x) = In(3x + 2)5 %3! b. y = (2x* + 1)tanx c.f(x) = etan(2x)

A: Explanation of the answer is as follows

Q: 9. If f is continuous and f(x) dx = 14, find f(2x) dx.

A:

Q: 11. Prove from the definition that the following functions are differentiable. ()- (b) f =xy?

A: By the definition, the function f(x,y)=xy^2 is differentiable if fx(x,y) and fy(x,y) both exist.

Q: If f(x) = In(tanh(2x)), then f' (x) is Select one: a. -2 coth(2x)sech (2x) :): b. – coth(2x)sech (2x…

A: f(x)=ln(tanh(2x))f'(x)= 1tanh(2x) ddxtanh(2x)we know that  tanhx=ex-e-xex+ e-x…

Q: If f(x) = etan-¹(x²) then f'(x) at x = 1 is equal to TU 2e4

A: The explanation of answer as follows :

Q: 1. Show that function f(x)=D|x | is not differentiable at 0

A: As per company guidelines we can solve first question. I hope that the given solution will help you.…

Q: C. Is the function define by g(x) = x² – sin x + 5 continuous at x = n?

A:

Q: 18 9. If f is continuous and f(x) dx = 14, find f(2x) dx. !!

A: Solution is in step 2

Q: If b > 3 and average value of f(x) = 6x – x² on the interval [0,b] is 6, then what is b equal to?

A:

Q: Show that f(x)= |x| is not differentiable at x = 0.

A:

Q: d. Find the linear approximation L(x) for f(x)=x²-x-1 at a = 1.

A: Given function is fx=x3−x−1. d We have to find the linear approximation Lx for function fx at a=1.…

Q: If g(g(x)) is continous at 0, then g(x) is continous at 0.  True or False?

A:

Q: Use the linearization of f(x) 1 at x = 4 to approximate f(4.3) . - f(x) =

A:

Q: Give the linear approximation of f(x) = x sin(nx2) at x = 2. Use this to estimate f(1.98)

A:

Q: The Second Derivative Test cannot be used to conclude that x = 2 is the location of a relative…

A: We need to check for which of the given functions, can't conclude about location of  a relative…

Q: 2 If f is continuous on [0, 2] and f(x) dx = 5, find the value of | f(æ – 2) dæ.

A:

Q: Show that f(x) := x/3, x e R, is not differentiable at x 0.

A:

Q: 2. Find the (exact) values of a and b so that f is continuous at a = 2. 8r2 + 20x + 28 if x 2

A:

Q: 34. Show that f(x) = Jã is not differentiable at x = 0.

A:

Q: If f(x)=e^cosh(4x) then f'(x)=

A:

Q: .3 Suppose that f is a continuous function and that f(x) dx = 6. Find f(3x)dx.

A:

Q: .For what values of a is Jaax - 2a, x z 2 f(x) 12, x < 2 continuous at every x?

A: Here given function  Since,  it is continuous for every x thus it Is also continuous for x=2