65. Two runners start a race at the same time and finish in a tie. Prove that at some time during the race they have the same speed. [Hint: Consider f(t) = g(t) - h(t), where g and h are the position functions of the two runners.]

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: Find f(x) if f(4) = -8 and the tangent line at (x , f(x)) has slope 7o* + 4. O a. f(x)= 7e* + 4x –…

A:

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

A:

Q: True/False: If ƒ is entire and |f(z)| > 2 for all z E C with |2| > 1, then f is a constant function.

A: If f is entire and fz≥2 for all z∈ℂ with z≥1Let gz=1fzas fz≠0 for any z∈ℂ⇒g is entire gz=1fz<12…

Q: 2. Ali is seated on the line which is normal to the curve f(x) = x² - 2x + 4 at the point (1, 3). 3.…

A: As per the company rule, we are supposed to solve the first three sub-parts of a multi-part problem.…

Q: 3. If f is continuous and f (x) dx = 8, show that the graph of ƒ intersects the line y = 4 at least…

A: The function f is continuous. The integral function is ∫13fxdx=8.

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: suppose f is a continuously differentiable function satisfying f(3)=6, and f'(3)=5. Find (f^-1)'(6)

A: Given f(3)=6, f'(3)=5  To find f-1'6 By the formula, f-1'x=1f'f-1x And we know that if f(a)=b then…

Q: If f(x) = In(tanh(2æ)), then f'(x) is %3D Select one: O a. coth(2a)sech (2r) O b. 2 coth(2a)sech…

A: Given: f(x) = ln(tanh(2x))…

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

A:

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

A:

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

A:

Q: Suppose F 1  and F 2 are both antiderivatives of f on an interval I How are  F 1  and F 2  related?

A: Given:  F 1  and F 2 are both antiderivatives of f on an interval I. That is,

Q: 4.1. Estimate f(3). 4.2. Estimatef'(3). 4.3. Give an equation for the tangent line to y = f(x) at x…

A: To estimate f(3), find the value of y when x=3 from the given graph When x=3, the value of y is 3.5…

Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

A:

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

A:

Q: 4) Consider the function 9 defined by g(x, y) = cas (7X Jj ) + logg(x-y) does 9 ha ve the maximum…

A: direction of maximum increase  Let maximum rate of change of a function f(x,y)  occur in the…

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: Use the limit definition of the derivative to compute p′(t) if p(t) = 2t^2−3t+ 1.

A:

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: 7. Suppose that f: R R is differentiable at c and that f(c) = 0. Show that g(x):= |f(x)| is…

A:

Q: 9. Show the function f(z) = 1 + 2i+2Re(z) is differentiable or not differentiable at any points.

A: Solution

Q: Suppose that fx) is continuous on [0, 9] and F(x) is an anti-derivative of f. If F(0)=9 and F(9)=7,…

A: Given that:                           f(x) is continuous in [0, 9].…

Q: let s(t)=3sin(2t)+5. find the absolute maximum and minimum of the function on the interval [0,2pi]

A: We have to find

Q: 55. Is the function given by S + 4, for x s 3, 2x - 5, for x > 3, F(x) continuous at x = 3? Why or…

A: Function is given by F(x)=13x+4 for x≤32x-5 for x>3 now show that it is continuous at x=3 or not.…

Q: Find the best quadratic approximation to f on the interval [ 0, 1].                     f(x) = x3

A:

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: 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: 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: 35. Given that f(z) is a continuous even function, then A 0 D

A: We will use the definition of an even function and properties of definite integrals to find the…

Q: 24, Find the domain of H function fw =J 2x+3 -1

A: Given,

Q: Find the values of k in f(x)=x^2-kx such that the line y=5x-4 is tangent to the function.

A:

Q: Suppose that f(x) is continuous on [0, 9] and Fx) is an anti-derivative of f. If (0)=9 and F(9)=3,…

A:

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

A:

Q: 2. Use a linear approximation to estimate V1.03. 3 If f and a are the functions whose gronhs

A:

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: 1 dt, for x > 4. In(t) Let F(x) 4

A:

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the g'(x) if: g(x) = 1 +t² dt 3x2

A:

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: Suppose it take aforceof 21 lb to stretch an industrial spring 3 ft from its equilibrium position.…

A:

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

A:

Q: Show whether the following function is continuously differentiable: f(x,y)=x2y2

A:

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: 1.) If the ball 1s Thrown vertically upward with a Veloorty of 15 m/s then ts heioht aifter t…

A:

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:

Q: Use differentials and the graph of f to approximate    (a) f (1.9) and (b) f (2.04).

A:

Q: 3. Let # 0, 0, r = 0. f(x, y) = Find f.(x, y), fy(x, y) at all points. Leave your answer as a…

A: We need to find differentiation of f(x,y) with respect to x and y.