Suppose that the functions u and w are defined as follows. u (x) =x²+5 w (x) = /x+7 |D Find the following. (u ow)(2) = 0 (w ou)(2) = [] ?

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: 5. Show that the function h(x, y) defined by if r2 + y? 1 is discontinuous.

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Q: Show that f(r) = O(|x – xo|*) and g(x) = o(]x – roP) imply f. g(x) = o(|x – xo]k+i). - -

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Q: 5. Show that the function h(r, y) defined by if + y 1 is discontinuous.

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Q: If we apply Rolle's Theorem to the function f(x) = 2x² – 16x – 5 on the interval [2, 6], how many…

A: Given,          fx=2x2-16x-5 on the interval 2,6.We know that,         Rolle's theorem states that…

Q: Let g=yf(xy). Show that: - дд у ду дд - Х = g дх -

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Q: Suppose that y is a function of x. Find if 2x°y 3 2y + 5. - -

A: We will find out the required value.

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

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Q: of and ду of For the function f(x,y) = In (x+ 3y), find

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Q: Find the Wronskian for the set of functions.{e3x, sin 2x}

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Q: If f(x) is a continuous function on [3,7] and F(x) is an anti-derivative of f(x) such that F(3)=7…

A: Given :f(x) is continuous function 3,7Fx is anti-derivative of fxF3=7 and F7=3To determine…

Q: Suppose that z = f(x, y) is implicitly defined as a function of x and y. Determine for 4x²z³ - 5yz²…

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Q: 8. Consider the function f(x)=/25-x² . a. Find the linearization L(x) of f(x) at x=3.

A: Given expression is , fx=25-x2 to find out the linearization L(x) of f(x) at x=3.

Q: Prove that f(x) = x 2 takes on the value 0.5 in the interval [0, 1].

A: We have to prove that f(x)=x2 takes on the value 0.5 in the interval [0, 1].

Q: Show that f (x) = 1 − |x| satisfies the conclusion of the MVT on [a, b] if both a and b are positive…

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Q: for x 2 - X Is differentiable at x = 2 but not at x = 1.

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Q: Suppose that the function f: [0, 1]  in R is continuous and thatf (x)>= 2     if 0 <= x <…

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Q: The graph of f(x)= x2 - 1 is concave down on interval | (-1,1) ^O (0,1) BO (-1,0) U (1, ∞ )co (- 00…

A: From the given problem:   fx=xx2-1   As we know that for concave downward:   f''x<0   So,…

Q: B)Is w = Zez analytical function or not?

A:

Q: Show that f(x1, x2) = 2 - (x1 - 1)^2 - e^x2^2 is concave.

A: the given function is fx1,x2=2-x1-12-ex22 To find the function is concave we have to show all its…

Q: Let g=yf(xy). Show that: - მყ У ӘУ дд - X- = g дх

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Q: For what value of x does the funciton g(x)= (1/3)x^3-2x^2 strictly convex?

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Q: 2 Show that the function f(x) = x-4x + 10x has no relative extreme points. 3X Relative extreme…

A: Given, Function: f(x) = 23x3-4x2+10x Differentiate f(x) with respect to x, we get: f'(x) = df(x)dx…

Q: 2.4 Use the definition of the derivative of complex function to show that f(z) is not dif-…

A: The Complex Derivative Definition: Let f be a function defined on a neighborhood of z0 ∈ ℂ. If…

Q: 5. Show that the function h(x, y) defined by 1 if a? + y? 1 is discontinuous.

A: We can solve this using R.H.L ≠ R.H.L

Q: Suppose f and g are differentiable functions on R such that, (x²+1)f (x) + 3xf(x) = e*2 + 7x and…

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Q: Suppose that the function f: [0, 1] in R is continuous and thatf(x) > 2      if 0<=X < 1.Is…

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Q: Suppose that ƒ(x) = x2 and g(x) = | x | . Then thecompositions( ƒ ∘ g)(x) = | x | 2 = x2 and (g ∘…

A: Given: The composite of the two functions are given as,

Q: Suppose that f(x,y,z)=x^2yz−xyz^3 is a function of three variables.

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Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 16/x on the interval [0,…

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Q: Find the value of c which satisfies the conclusion of Rolle's Theorem with the given f (x) =x³ - 3x,…

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Q: Suppose that f(x, y) = yVx³ + 1 on the domain D = {(x, y) | 0 < y <x < 3]

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

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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: Suppose h(x) = [,f(t)dt on the interval [0, 12], where f (t) is shown in the graph below. f (t) -4-…

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Q: Compute the linearisation l(x) of f(x) = √1+x3 at x=2 and use this to estimate f(2.05)

A: Given function is: fx=1+x3 At x0=2 So the linear approximation is: Lx≈fx0+f'x0x-x0…

Q: ) The domain of the function y = In(1 – x²) is R – [-1,1].

A: Log (x) is defined for every  x is positive real number .

Q: Find f(x) if f(3) = 0 and the tangent line at (x, f(x)) has slope x2 + 5 In (14) f(x) =| 히n 글미(구+ 5)…

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Q: Suppose f is differentiable with f(0) = 0 and 0 0.

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

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Q: If 5х + 3,х <2 { h(x) = 2x2 + 5,2 < x < 4 Is h(x) continuous at (x=2)?

A: We use definition of contunity

Q: Q.4 A/ Prove the function continuous at x = -2, (x2 + 5 13-3x where %3D if x<-2 if x 2-2 f(x) = %3D

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Q: 1. If f(x) = x + v2 – x and g(u) = u + /2 - u, is it true that f = g?

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: Find f•g and g of , where f (x) = x^2 + 1 and g(x) R to R. =x + 2, are functions from

A: To find f0g and g0f where f(x) and g(x) are real valued functions from R to R

Q: Suppose that x = x(t) and y = y(t) are both functions of t. If 22 + y = 20, and -1 when x = 2 and y…

A: x2 + y2 = 20 Differentiate with respect to t 2x dx/dt + 2y dy/dt = 0 In this equation we put x = 2,…

Q: Let S(x²+2x)², x> 1, f(x) = Tax+ bx², ах x< 1. Compute for all a and b such that the function f(x)…

A: Proceed as shown

Q: Suppose that a function f(x, y) satisfies fxx fyy – (fxy)² > 0 at a point (a, b). How is the sign of…

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.