- 12 110 - 4 10 16 -- - 2 a) gl-1) = a(1) = = (1) 16) = b) domain Range c) find values of for g(x) =4 ds find valves of x for glx)74

Q: True or False: If fe L'(T), then {f(n)} € {(T). Fill in the Blank: If " g(x)2 dr < 4, then l@(n)²<

A: Given that, f∈L4(T) Then this can be written as, f=∑n=1∞|an|4 By using the cauchy method, f(n)∈l2(T)…

Q: 13 Which function can the chart below belong to? A) y = x^ {1/3} (y =x to the {1/3}) t0 13 - B) y =…

A: In option A, the given function is y=x13 The table of values is: x y -1 -1 0 0 1 1 2 1.26…

Q: Question number 2.

A:

Q: to set Up Tutoring: (888) 1. Take the derivative of y = (7+x)(7+z) select Derivative does not exist…

A: The objective is to find the derivative of y=(7+x)(7+x)2 .

Q: Find f'(x) and f"(x). f'(x) f"(x) = f(x) = (x³ + 7)ex

A:

Q: 6 f(x) = 7 + find f'(x). Find f'(2).

A: As we know that: The sum/difference rule: f±g'=f'±g' The Power law: ddxxn=nxn-1 Given: fx=7+6x+2x2

Q: If ƒ(x) = (6x² – 3)¹, find: f'(x) = ƒ''(x) =

A:

Q: 9) Determine the third derivative with respect to x for y = In x 10) Given f(x) 2x + 1 and f(1) 4.…

A: Find the derivative

Q: If ƒ(x) = (x² + 3x + f'(x) = + 3x + 2)², then ƒ' (2) =

A:

Q: shown in the figure. Where is f'(x) < 0?

A: Given graph of function is

Q: 7. (a) cosh?1 (b) 2 sinh² 20

A:

Q: A) Which X-vakes in the interval (3,3] gire: max f'(x) Interval [-3,3) gives: BWhich b in the min 5…

A: Consider the given graph of the function.

Q: Find a function f(x) such that f'(x) = 4x² + 5 and f(0) f(x) = = 3

A:

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 16) y = (x2 - 2x + 1) eX B) (x2…

A:

Q: 3) Using Quotient Rule ()'=€'gfg),find (±)' = (3×/eX)' = A) (3/e)X[In3-1] B) (3/e)x-1 C) 3×ln3/eX D)…

A: Topic:- derivatives

Q: '5 7 f(x) dx = 11, evaluate 15 Given f(x) dx = 19 and 7 (a) f(x) dx.

A: Given : ∫05fxdx = 19∫57fxdx = 11

Q: 8) GIVEN THAT F-x²yax -yay, FIND&F-d/ WHERE L IS THE COUNTOUR SHOWN IN THE FIEURE. 3 2 1 2 3 4

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Q: Given f''(x) = 8x + 6 and f'(0) = 1 and f(0) = 2. Find f'(x) =

A: f''(x)=8x +6integrating w.r.t. x;∫ f''(x) dx =f'(x)f'(x) =∫ (8x+6) dx        =8x22+6x+Cf'(x)…

Q: 7.) f (x)> (3x+2)(5x-2)

A:

Q: 2 9. If f(x) =-(x- 5), determine the following %3D 3 f(17)- f(8) а) 17-8 (12)- f (4) b) 12 - 4

A: The given function    f(x)=23x-5

Q: Given that x - 4 g(x) x + 3' find each of the following. a) g(5) c) g(-3) b) g(4) d) g(-16.2

A:

Q: 12)The range of the function f(x) = sinx -1-2 is the interval : a)o 치 b) (x+10) {(a-10)] c)O d) O…

A:

Q: Let f and g be two differentiable functions. Suppose we know that f(2)=5, f'(2)=-2, f(1)=–3,…

A:

Q: Find f ogohif f(x) =, g(x) = x", h(x) = x + 3. 10 x+1'

A:

Q: Skerch a porsiblea raph aea fmaion informanion beiow. anur I maxma,1dcaiminim…

A: Step:-1 Note:- 1. Inflection Point:- An inflection point is a point in which the concavity of the…

Q: 4. a) Solve the equation 5sin-'x- 2n = 2sin-'x-3n 6) Graph, find x where f(x) = g(x), bounded by…

A:

Q: Given f'(x) = x²(x+2)(x-2)' find the x- coordinate of any relative max / min or Pl. lo noitoaltni lo…

A:

Q: Derivative. The derivative of h(x) : 3+ e(4x2 + 5) is O none of the other answers -e(4x + 5)…

A: step 2 complete solution

Q: 13) 16) x2/3 x + 1 x³ x² +1 dx dx

A: Given data:- 13) ∫x23x+1dx 16) ∫x3x2+1dx

Q: If f(3) = 5 and f'(x) ≥ 2 for 3 ≤ x ≤ 8, how small can f(8) possibly be? f(8) Z

A: f(3)=5f'(x)≥2    for 3≤x≤8

Q: 3 5. If f(x) = and g(x) = 4*, find: X-4 a) f-¹(g(x)) b) the domain and range of f-¹(g(x))

A:

Q: 4. 3x³y + 2y³ = at y = -2. 9x² dx +by+ dx = U_01-5 Find the slope of the tangent line to the graph…

A:

Q: 6. Prove the following identity: n ()-(7)-(-)) (" + ¹) + (x − ¹). k k-1, k

A: The objective is to prove the identity:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.