4. Evaluate: [ 1 dt. Vt2 –6t+13

Q: (ux – u² – x²) dt max subject to х %3D х + и, х(1) 3 2.

A: As per the question we are given a optimization problem, and we will find the optimal control law by…

Q: 2. Find t+2 dt check your result by differentiating

A:

Q: Let H(x) = | V49 -P dt dt, for - 7sxs7. a. Evaluate H(0). b. Evaluate H'(6). c. Evaluate H'(7).

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: compute ∫_∂D(x^2ydx+xy^2dy, where D is described by 0≤x≤1, 0≤y≤x

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Q: Find F'(x). F(x) = dt t4

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Q: Find the value of " dt 2 at the point (0, -1) if xy + y? = 1 5.

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Q: I'(x) p-let dt,

A: Γ 12=2×∫0∞e-u2 du Here, Let's calculate the value of Γ 12, The gamma function is defined as Γ…

Q: Differentiate ysin(1/y)=1-xy

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Q: Compute the partial derivatives. f(x, у, 2) %3D 8x4 y7 + z6 af 3 32x 17 +-6 af – 56x ду _6 48x4 y'…

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Q: Let F (x) = (1 + t2)/4 dt - Then %3D F'(x) =

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Q: If f(z) = (t³ + 5t2 + 3), dt then f''(z) =

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Q: Find the four second partial derivatives. z = 7x2 + y9 ax? azz дхду дудх az ay? %3D II II II

A: We have to find the four second partial derivative of the given function. The given function is…

Q: 2 =1+ %3D V1+f(t) dt, x 21

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Q: Find the linearization of f(x) = 9 – dt at x = 1. 2+t

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Q: Integrate f(x, y)

A: The region is defined as, Consider the conversion formulae from cartesian to polar coordinates,…

Q: 2z Forz> 0, 순(/"m(P + 1) a) In (t³ + 1) dt For x > 0,

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Q: Find F'(x). 1. F(x) = √x+² (4t + 1)dt 2. F(x) = f*t³dt SOLUTION IN HANDWRITTEN

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Q: 4) Determine the function F(x)=[ƒ(1)dt, where ƒ(x)=sgn(x-x²) for xe[-1,2]. -1

A: f(x) is discontinuous but F(x) is continuous

Q: Find the linearization of f(x) = 3+ S" sec(t - 1)dt at .2 END x = -1

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find f, and f,. f(x, y) = 13x In xy

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Q: 6) If y=x² +1+ f dt , prove that y"= 2 - x2

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Q: If f(x) I (t° + 2t + 6) dt 0. then %3D = (x), ,f

A: The function needs to be integrated first and then to the subsequent function we will be double…

Q: ư (yũ + Vũ) du =

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Q: Eliminate the arbitrary constants a. x = -In t, y = at + bt?

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Q: Evaluate f 26t 3 dt where B is a real valued constant.

A: As per guidelines, I can answer only one question.

Q: Find a value of x such that

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Q: Find du -if v = t- dt

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Q: 4. F(x) = (1- t) dt %3D 4

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Q: Let f(r) = Vt3 +1 dt for r2 3. 3

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Q: 3t – 2 dt t + 1

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Q: | f(t) dt 20z 4, then f (t) dt is If 4x²+21

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Q: 8. Find the orthogonal trajectories of y = cx CX

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Q: Q, Frd the donain of H fallowing function: fa) = 5x -3x-4

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Q: Find the interval on which the curve 1 dt 4+t+ 2t2 is concave upward.

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Q: which is the best definition of a counterexample

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Q: Find the linear approximation 0 to Write your answer in the form y = Ax + B. at x =

A: Explanation: The Linear Approximation should be a line that can substitute (in a narrow interval)…

Q: What is the linear approximation for any generic linear function y=mx+b?

A: Given: y=mx+b

Q: 8) Confirm that the stated formula is the linear approximation at x =0 %3D (1+x) =1+15x

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Q: At time 0, M is deposited into Fund X, which accumulates at a force of interest δ# = 0.006t*. At…

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Q: In (secx) a) | sec2t dt + cot x

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Q: Find ds/dt if t = sy1- s2

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Q: If f(x) = | (3 + 4t + 5) dt %3D then f'"(x) =

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Q: a) Use the definitlon of derlvative to find ds If dt 2t+1

A: As per bartleby guideline for more than one question asked only first is to be answered please…

Q: Find F '(x).

A: The given function F(x) is,

Q: Find (f1)'(0). dt f(r) ((0) =

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Q: Find F'(x). 'x+7 F(x) = (6t + 7) dt %3D X1

A: Fundamental theorem of calculus If F(x)=∫af(x)g(t)dtThen,F'(x)=f'(x) g(f(x))

Q: 13. Prove that the function 2x 1 dt t F(x) is a constant on the interval (0, ∞ )

A: The student has specifically asked for the solution to Question-13. Hence, that question is solved…

Q: Let F(x)= | V1+P dt. Find F'(5). x,

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Q: f(x, y) = /32² + 3y fz(4, 5) = VT23 %3D

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Q: Integrate f(x) = 10 ( 1 – x)9 where 1 ≤ x ≤ 3, Using Boole’s rule

A: The function f(x)=101-x9 where 1≤x≤3. We have to integrate this integral using the Boole's Rule.

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.