Let f be the function defined as follows. y = f(x) = V9x + 1

Q: Let be a derivable function and h '(x) = g (x2 +1). Calculate h '(1) if g' (2) = 5.

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Q: Find a function f such that f ' (x ) = x 3 and the line x + y =0 is tangent to the graph of f

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

A: We have given function fx=e-x As we know the modulus function is not differentiable at x=0.…

Q: Find the function f (x), given that f'(x) = vx + x² and f(0) = 2.

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: ) Find a function ƒ such that f'(x)= x³ +3 and such that the line y+5x O is tangent to the graph of…

A: Given, f'(x) = x3+3  and the line  y +5x =0 is tangent to the graph of f   Let's assume the function…

Q: the function f is not differentiable at x=0.

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Q: 1. Determine and sketch the domain of the function f(r,y) = e2/Vy¬I, What is the range of f?

A: So, given function is    f(x, y) = e-x/y-1     here,  y should strictly be above 1    and then it…

Q: Estimate the IROC for the function f(t) =Ax) = x² – 20x

A: Given: fx=x2-20x To find the instant rate of change, Differentiate the given function with respect…

Q: Is the following function continuous? [x² + y² _if x² + y² ! f (x, y) =

A: The left-side limit, the right-side limit, and the value of the function at that point can be…

Q: The function f(z) is analytic if

A: analytic functions are functions which are locally given by the convergent power series. i.e any…

Q: Let be a derivable function and h (x) = g (x2 +1). Calculate h '(1) if g' (2) = 5.

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Q: Locate the discontinuities of the function. 2 f(x) = 1 + e7/x

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Q: Find Fxxygy for the function Fory)-J*J€nx-x]

A: We havr to find the derivative.

Q: for function f(x) = e=z²/(20²) sketch f(x)!

A: Topic :- Calculus

Q: Find the value of the constant (a, b, or c) that makes the function continuous.

A: A function fx is continuous at x=a if its left-hand limit, right-hand limit, and fa are equal and…

Q: Determine the interval (s) on which the function f(x) = 3xe* is concave down. O 号

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Q: Differentiate the function y = In [(x* – 1)(x² + 1)²] to the simplest form. - The number of online…

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Q: Let f : Z+ → N be the floor function f(x) = [(x – 1)/2].

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Q: Find the graph of the function f(x) = [x] + [x/2] from R to R.

A: Given function is fx=x+x2. Definition: Floor function is the greatest integer that is less than or…

Q: What is T3 centered at a = 3 for a function f such that f (3) = 9, f' (3) = 8, f'' (3) = 4, and f'''…

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Q: Let f(x)=x²+x. Compute f'(2) using the definition of the derivative, f(a+h)= f(a) f'(a)= lim h 0 h

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Q: Let the function f: R → R be defined by 1 x² f(x) = - 0, x = 0, x = 0.

A: Let us solve the given problem on continuity in the next steps.

Q: . Suppose that f(r) is a function given by for 0<r<7, f(z) = for -n <I<0.

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Q: 2. Use the graph of the function f(x) to estimate where (a) f'(x)= 0, y f(x) (b) f'(x) 0.

A: (a) f'(x) =0   =&gt; the slope is zero, it means when the graph is parallel to x-axis  i.e. at…

Q: Let A(x) f(t)dt, with f(x) shown in the graph below. -3- ** * T?

A: As per the fundamental theorem of calculus, given a function A(x)=∫0xf(t) dt, the derivative of this…

Q: sketch the graph of the given function on the interval t ≥ 0.  2.g(t)=f(t−π)uπ(t),where f(t)=t2

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Q: Consider the function f(x) = 12x+ 45x - 200x + 3. f(x) has inflection points at (reading from left…

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Q: Let f(x) = V9 – 2x. Find f'(x) using the limit definition of the derivative.

A: To find f'(x) by definition f(x)=√(9-2x)

Q: Why is ƒ not a function from R to R if f(x)= ½? b. f(x)= Jx ? c. f(x)=±/(x² +1)? а.

A: Why is f not a function from R to R if,  a) f(x)=1xb) f(x)=xc) f(x)=±x2+1

Q: +V2x y =

A: According to the chain rule of differentiation:

Q: a) Investigate whether the function f(z) = z is analytical?

A: In order to investigate whether the function is analytical or not, first write the function f(z) in…

Q: Find a function f such that f′(x)=2x^3 and the line x+y=0 is tangent to the graph of f.

A: Solved below

Q: make a sketch of the given function on the interval[0,∞).

A: Given: To Plot:

Q: Find a function f such that f′(x)=−3x^3 and the line x + y = 0 is tangent to the graph of f.

A: Given: F'(x)=-3x3 and the line x + y = 0 is tangent to the graph of F            We know that…

Q: Consider the function f(x) = z + 6

A: Givenf(x)=1x+6

Q: On what domain is the function f(x) = – 4+ v–48 – 6x continuous?

A: The given function is: f(x)=-4+-48-6x

Q: Let g(x) = re) dt, where f is the function whose graph is shown. y f 2 12 2.

A: Consider the given equation:

Q: Verify that fy =f for the following function. %3D f(x.y) =*y+5

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Q: 1. Why is f not a function from R to R if a) f(x)= 1/x? b) f(x) = T? c) f(x) =±V(x² + 1)?

A: We'll answer the first question since the exact one was not specified. Please submit a new question…

Q: Find the inflection point(s) of the function f(x) = 2eX. %3D (x, y) (smaller x-value) %3D (x, y) =…

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Q: Consider z as function of the variables x and y, it is defined by :

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Q: f(x) = x3+x

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Q: Assume that we have functions f(x) and g(x) so that

A: Given functions - ∫-13f(x) dx = -1∫35f(x) dx = 4∫-11g(x) dx = 3∫15g(x) dx = 2∫-152f(x)-5g(x)dx = ?

Q: Let A(z) | f(t)dt where f is the function given by the graph below. -2- -3 -4+ to

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Q: The function f(x) = k is continuous.

A: Given f(x) = k

Q: of find and of For the function f(x,y) = x+ 8y ду

A: Function given is- f(x,y)=6x+8y To find- ∂f∂x and ∂f∂y ∂f∂x=Partial derivative with respect to  x…

Q: Find all the extreme values and their types from the function f defined by f (x, y) = 2y3 + 2x3 -…

A: Given: f (x, y) = 2y3 + 2x3 - 3xy2 - 12x

Q: Q3) If f(z) is analytic function and u(x, y) = x - 3xy find f(z) |

A: We have to find analytic function using C-R equation.

Q: Consider the following function f(x) = (2x + 3) e* Find the equation of the tan gent line to the…

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Q: Let A(x) = f(t)dt, with f(x) shown in the graph below.

A: Given that: Graph of f(x)