For cach of the following functions, simplify 5) f(x)= *6) f(z)=

Q: For the following function f(x,y) = A/x^2+y^2  find fyy(x,y)

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Q: ): Apply Rolle's theorem for the function f(x) = 9x² – 36x + 27 over the interval [1, 3]. Justify…

A: Given :- Apply Rolle's Theorem for the function fx = 9x2 -36x + 27 over the integral 1,3.

Q: Find the values of a and b that make the following piecewise defined function both continuous and…

A:

Q: Suppose f is a function where the line tangent to it at x = 3 is given by y = 5x + 2. Find the…

A: Given information: y=5x+2,  Find the value of f(3) and f'(3)

Q: Suppose that f(x) is a differentiable function and g(x)=(x+2)/f\x). If f(0)= 22 and f(0)=5, then…

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Q: Suppose that f is a function given as f(x)=x3+bx2+cx−4 Find the exact values of b and c if we know…

A: Given: fx=x3+bx2+cx-4   and tangent line y=36x+68

Q: Find an equation for f(x) using the tangent function. f(x) = f(x) 12- 10 8. 6. 4 2 X 3 2 6. 6 3 6 -8…

A: The given graph is:   To find the equation for f(x).

Q: Find the inflection point(s) of the function f(x) = 3e-X. 1 1.8196 (х, у) x ) (smaller x-value) %3D…

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Q: Given the functions Az) = cos(x) and g(z) = x - 5x- 6, determine the domain of the combined fx)…

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Q: Use the definition of derivative to find f'(x) for f(x) = ax² + 10. f(x+h)– f(x) | f'(x) = lim h0 h

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Q: 2. (a) Define what it means by for y = f(x). %3D

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Q: Given the function f (x) Find limAr0 z+3 f(x+Az)-f(x) Az

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Q: 9. Show that for f(x) = x° we have f"(0) = 0 but the point x = 0 is not an inflection point of f.

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Q: Let f be defined as follows: x2 +5 for x > 5, Зах f(x)3D for xs5 For what value of a is the function…

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Q: but f'(x) is never equal to 0. Why

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Q: Suppose that f(x) is a differentiable function such that f(8)=7 and f(8)=1. If g(x)=sin(f(x)), then…

A: Given,

Q: if f(x) is a function that is continous at (2,f(x)) then f(x) is differentiable at (2,F(2))   true…

A: Given statement is If f(x) is a function that is continous at (2,f(x)) then f(x) is differentiable…

Q: On what domain is the function f(x) = – 4+ V3x – 6 continuous? %3D

A: The function is a square root function and hence, the function is continuous in the domain.

Q: Differentiate the following function with respect to X. eX + 3Y =1

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Q: Suppose, f'(x)=2cosx+ sec x, -7<x<7½, and it is known that f(T) =D4. Find the function f(x). IT

A: Integrating on both sides, we get

Q: The function f(x) = x^2 is decrea sin g on (- ∞,0)  True or False

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Q: Determine if the following piecewise defined function is differentiable at x = 0. 4х- 1, X20 f(x) =…

A: We will check whether the function is differntiable or not at x=0 as following.

Q: 1. For f (x) = Vx + 1, g (x) = vx – 1, find the domain and range of f,g,f + g,f •g

A: Domain: The set of all the values of x for which the function is defined or exist.…

Q: For what value of the constant c is the function f continuous on (-0, 0) if x < 5 f(x) ={ cx? + 8x…

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Q: Suppose that flx) is a differentiable function and g(x)=(x+2)/f(x). If f(0)= 22 and f(0)=5, then…

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Q: The function f(0) = tan 0 is not defined for multiples of

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Q: Given that flz) and g(z) are concave down functions. If we define h(r) = f(r) + g(c). Then h(c) is a…

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Q: Suppose that f(x) is a differentiable function such that f'(8)=7 and f(8)=1. If g(x)=sin(f(x)), then…

A:

Q: The Range Rf for the functionf (x) = tanhx is:

A: Range of f(x)= tanh x

Q: Suppose f(x, y) = 2 sin(11xy) and g(x, y, z) = v144 – x2 - - Find the following function values. f…

A: Suppose f(x, y) =2 sin(11xy) and g(x, y, z)=√(144 - x2 - y2 - z2) To find the following function…

Q: For the following​ function, make a table of slopes of secant lines and make a conjecture about the…

A: Topic:- application of derivatives

Q: Given f(x) = Vx and g(x) = |x – 2|, find 9. Determine the domain of the function in interval…

A: Given function :

Q: The area of a disk as a function of radius is given by A = πr². How close must r be to 2.0 cm to…

A:

Q: . Give a function f (x) which tends to 0 as x tends to infinity.

A: We have to find a function which tends to 0 as x tends to infinity.

Q: Show that the function is discontinuous on R. f(x) = { 1; 0; for x € Q for a Q

A:

Q: On what domain is the function f(x) = 3x + 5x + 6 continuous?

A: The given function is, fx=3x2+5x+6

Q: Determine f ″ ( x ) for f(x) = sec x

A: Given function: fx=secx

Q: If f(x) = 7cos(x), what is f'(x) ?

A:

Q: 2) For the function below f(x)=7x1.1^x, estimate f'(x) using h=0.001 for the following three values.…

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Q: - Given f(x)= -, find f(x). 2+x %3D 6.

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Q: If f(z) = 4,/ In(x), find f'(x). Find f'(2).

A: Given function:fx=4xlnxWe need to find f'x and f'2.We will use the following…

Q: Show that f x) = Ix- 5| is NOT differentiable at 5 by using the definitien of the derivative, (Start…

A: Definition of derivative:f'(x)=limh→0 f(x+h)-f(x)hf(x)=x-5f(x)=5-x,  x&lt;5x-5,  x≥5L.H.S.…

Q: Find the points of inflection for the following functions if they exist: f(x) = 3x2 + 2 cos(x), f(x)…

A: Here is the solution of the given problem. Point of inflection of the given function f(x) is the…

Q: Find the value of the constant cc that makes the following function continuous on (−∞,∞)(−∞,∞).…

A: We have been given a piecewise function and we need to determine the value of ‘c’ at which the given…

Q: Given that f(x) = 4x2 − x + 2, use the limit definition of the derivative to compute f'(x).

A:

Q: 42. For f(x) = cosxsinx, determine all of the values of x for which f(x) 0

A: Recall the trigonometric identity shown on the white board.

Q: Suppose f is a differentiable function such that f(g(x)) = 5x and f'(x) = 1 + [f(x)]³. Find g'(x).

A: We have given f(g(x)) = 5x and f'(x) = 1 + [f(x)]³.

Q: Let f (2) = 2 22 +6 x + 5 . We will use the definition of derivative to find the deivative of f (æ)

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Q: For #6 and # 7, use the second derivative test to determine where the curve is concave upward and/or…

A: Please see the explanation below.....

Q: For the function f(x) 5x³ – 8x² + 8, , Step 1 of 2: Find the slope of the tangent line at x = 1.

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.