Let f(æ) = (4x + 26) In(æ + 3) %3D for æ > -3. Find the smallest value of A so that f(a) is concave upward on the interval (A, oo).

Q: Consider the function f(x) = 2x10 + 7x° – 6x² – 9. Enter the antiderivative of f(x) -

A: To find The anti derivative of f(x).

Q: find f given f (z, y) = e + 2ry 4y at (0,3)

A: Topic- partial differential

Q: Find Tn centered at x=8 for all n for the function f(x) = ex

A:

Q: Let f (x, y) = xy2 + 5. Evaluate df/dy at (x, y) = (2, -1) and interpret your result.

A: Given: f (x, y) = xy2 + 5.

Q: Fundamental Theorem of Calculus.

A: ∫abfx dx

Q: Please

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Q: dy from t dx n for y as a function of x, and find two results are consistent by expressing the (a)…

A:

Q: Use the linear approximation of f(x) = at r = 0 to approximate f(-0.1). 1+r

A: Use the linear approximation of f(x)=1/(1+x) at x=0 to approximate f(-0.1).

Q: Consider the function f(x) = 5a°+ 5x® – 10x4 – 6. Enter an antiderivative of f(x)

A:

Q: Let F(x) be the function defined as follows: F(x)= (1+ In(t))*dt What is the value of F'(e) ?

A:

Q: The function f(x) has the following properties at x,: Af = 0.23751 and 0.24369, where h=0.1. Find…

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Q: Is the function F (x) = L", e“ dt concave (concave down) or convex (concave up) for x<0?

A: To solve the following problem

Q: Differentiate the function with respect to the independer X f(x) = +e5x + e 2 e (x) = 0

A:

Q: Find a value of x, if any, at which f(x) = Vx – 27 is not continuous.

A: f(x) = (x-27)(1/3) To find :- Value of x where function is discontinuous

Q: State the interval(s) over which the function f(x) = V16 – x² is continuous.

A: Given, fx = 16-x2   We have to state the interval over which the function is continuous.

Q: Suppose that f(x, y) : at which {(x, y) | 0 < x < 4, – x < ys va}. 1+ x D

A: Consider a given function:  The objective is to evaluate the following double integral of fx, y…

Q: Find the linear approximation to f(x) = cos(x) near a =- [Where L(x) = f(a) + f'(a)(x – a) ] 3

A: Solution: The objective is to find the linear approximation

Q: Verify the final value theorem of f(t) =1+et[sint + cost]. O- 1 1

A:

Q: Let F(x) be an antiderivative of f(x). If F(1) = 12 and f (x) dx = 17, what is F(4)?

A:

Q: Consider the function f : RH→ R defined by f(x) = 2e(2z+5) log(2r+5) + If f convex or concave ? Why…

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Q: dx Show that f - In|ax + b| + C where a # 0. ax+b

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Q: find given f (x, y) = eª + 2xy² – 4y at (0, 3) af dy'

A:

Q: Differentiate. f(x) = In (In (In (7x))] f'(x) =D

A: Find f'(X)

Q: Find the linear approximation of f(x) = In r at a = 1 and use it to estimate In(1.14). L(2) = %3D…

A: Please refer the attached image for complete solution.

Q: Let f(z) (x-iy)e- ) Determine the points at which exist, and find r(2) at these points.

A:

Q: Show that the subtangent of f (x) = ex is everywhere equal to 1.

A: Formula to find the subtangent of the function helps to find the required subtangent. Derivative of…

Q: Q2 (A) At what points f(x, y, z) in which the function f(x, y, z) = continuous? is

A:

Q: Find the best linear approximation to f on  the interval [-1,1].                        f(x) = x2

A:

Q: Show that f(t) dt ) dx (x - a)f(x) dx.

A: To prove: ∫ab∫xbftdtdx=∫abx-afxdx

Q: Calculate the approximation of My for the given function and interval f Cx)=フメーンLュ,3 %3D

A:

Q: Consider the function F whose criterion is = / dt. 1+ t2 F(x) sena When determining dF/dx the result…

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Q: Given a2 +1, x 1. Is f differentiable at x = 1? Is it continuous at x = 1?.

A:

Q: Establish the interval where the function h ( x) *x° + 1 is concave down (CD), and find its point of…

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Q: Find the interval(s) where f is concave up for f(x) -4x4-3x- 5x-10 0)

A:

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

A:

Q: Consider the function f(x) = 7x° + 9x° – 9 - 9. Enter the antiderivative of f(x) + C

A: T

Q: Consider the function f(x) = 9x° + 9x' – 10a? – 4. An antiderivative of f(x) is F(x) = Ax" + Bxm +…

A: Given: fx=9x8+9x7-10x2-4

Q: Q: Which c.d.f. F is of X is continuous at x=0?

A: If F(0) = F(0-) then F(x) is said to be continuous at x = 0

Q: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of at x = 1. %3D df-1 - dx

A:

Q: Consider the function f(x) = 6x' + 8x5 – 10x³ – 6. %3D - Enter the general antiderivative of f(x)

A:

Q: Let f(x)=.062x4 + .38x² – 13x +39. Using linear approximation centered at 10, approximate f(10.195).

A:

Q: Consider the function f(x) = 12x' + 60x 100x + 6. f(z) has inflection points at (reading from left…

A: Here, f(x)=12x5+60x4-100x3+6

Q: f(x, -0.0494 -0.3662 etter estimates by using Ar = 0.01 and Ay = 0.01. %3D 0.0516

A: Here we have to use difference quotients with ∆x=0.1 and ∆y=0.1 to estimate the fx(1,3) and fy(1,3)…

Q: Find the values of a and b such that f is differentiable at x = 3

A: Given,            The function is fx=ax+bx≤32x1-1x&gt;3To find : Find the values of a and b such…

Q: If f(2) = 14, f' is continuous, and f'(t)dt = 23, what is the value of f(5)=? %3D

A: Given :

Q: Calculate the error of approximation E, for: f(x) = v3x + when x = 8. Ax = dx = 0.1

A:

Q: [a, b]. If F(x) is an antiderivative of f(x), for real numbers ¤) + k]dx is equal to

A:

Q: Assuming that f(x) dx = 3, f(x) dx = 4, and f(x) dx = 8, calculate Fx) dx. %3D %3D Jo f(x) dx =

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.