Eliminate the parameter t from the following. x(t) 3 tant y(t) = 3 sec t

Q: 8) Find all values of t for which x = +5, y = t lnt – t has a vertical tangent line

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Q: 4) Consider the curve given by: cos(xy) = x(y – 7) – 1 a) dy Find y' xp dy dx b) Find an equation of…

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Q: 1. If an object moves with velocity v(t) = sin(t) + 3t and begins at position p(0) = 0, find the…

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Q: Q.5/ A) Find dx for the following equation y = In(x2 + 4) – x tan-() %3D

A: Given equation is y=lnx2+4−xtan−1x2 We have to find dydx. Used Formula:- ddxlnx=1x ddxtan−1x=11+x2…

Q: You tart muesting at t=0 y co) =0

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Q: H.wl: Find L{e-3t St. sin 2t.dt p1 p2

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Q: Q3 Find dy/dx on the graph y3 sec/x2 + y2 = cos2x at point (1, 2).

A: The given function is, y3secx2+y2=cos2x

Q: Express in the form y = f (x) by eliminating the parameter.x = t, y = tan^−1(t^3 + e^t)

A: Given:             x=t, y=tan−1(t3+et)

Q: 2as L{t sin(at)} = %3D (s²+a²)²

A: We can derive it using the definition of Laplace transform or by using some identify or formula.

Q: 24.(cos t) y″ + (sin t) y′ − ty = 0

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Q: (b) S¤(tan? #)dx (c) S cos(2t)e'dt (d*) S(arccos x)²dx (e*) S (1+ 3x)2 dx Hint: Check for a similar…

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Q: 1- find dy/dx as a function of x. y = sec (tan x) 2- find dy/dx etty = 2x + 2y %3D 3- find an…

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Q: 1. Find for y defined implicitly by the equation dx

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Q: (2 – 4t) sin() tan(2r) V17 – cos(2nt) Find the equation of the line tangent to the graph of f at r =…

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Q: 2+x 9 y = Arctan( ) 1- 2x 10. x = cos't ; y = sin't

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Q: T/2 S cos (x) sin°(x) dx = %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: dw (C): If w = tan x and x = 4t³ + t ; Find ? dt

A: Let's do derivative of given function.

Q: Find dy and evaluate when x = T and dx 0.5 for the function y -10 cos (5x)

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Q: T/2 S. CoS (x) dx

A: solution in step 2

Q: B-The result of dy/dx for the following function is cos x y = 1+sin x

A: We have to find out derivative

Q: 5. x = cos 2t, y = sin 2t, 0 <t< T

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Q: 14. Solve the equation d?x dx dt +2x sin 3 dr? dx given that at t= 0, x = 0 and %3D dt ment

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Q: B-The result of dy/dx for the following function is COS X y 1+sin x

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Q: Q3 Find dy/dx on the graph y3 sec /x2 + y2 = cos2x at point (1, 2).

A: We have to find the derivative  of given expression at point (1, 2)

Q: •T/4 t4 tant dt 2 + cos t -T/4

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Q: 6. Find the derivatives of the following: a) g(r) = sin(vi) dt %3D g(=) = /" Ve +4 dt

A: Please refer to the image below

Q: find dx/dt x=(cos2(t/2))

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Q: 8. Find the length of the curve defined by x = cos(2t), y = sin(2t) from t = 0 to t = n.

A: If x = f(t), y = g(t) in (a, b) then length of the curve is,

Q: The equation implicitly defines y as a function of t. Find dy dt 1² sin (7 y) = -8

A: This question is based on implicit differentiation.

Q: 4. Find d²y/dx² for the following functions: a) y = sin x? cos 2x

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Q: 4. Find d?y/dx² for the following functions: a) y = sin x² cos 2x b) y = cos*(sec² 3x) c) y = x²(x³…

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Q: Find e-t sin(v3t) (a) L dt (b) L-1 -1 tan

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Q: 18. dx/dt = e'(1 + sin t)/(1 + cos t). Answer: [x – e' (tan(t/2)) = C]

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Q: given dy=x+coS X find yuhere y( -1.

A: Using variable separable.

Q: 1. Find the derivative (dy/dx) of the following functions: a) xy = cot xy b) x cos(2x + 3y) = y sin…

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Q: Solve the given problem below: (2x + y cos x) dx +sinx dy=0

A: We will solve it by exact differential equations method.

Q: 5. Find G(1), G'(0), and G'(1/4), where G(x) = | tan t dt.

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Q: cos(5r)ő(1 – 3) dt = e sin(t)6(t – 2) dt =

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Q: 4) e (). – | T|x² – 4| CoS - 2 2x sin sin² ( T|x² 19 dx 2 -3

A: Integrate

Q: 4t S = -2 С. t+1 1+sin 0 2 d. r = 1-cos 9

A:

Q: 2. Find the first and second derivatives of the following functions a) y = 6) y = e", c) y = In (sin…

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Q: Q5) a) Use potential function to evaluate the following. e* Sin(y) dx + e*Cos(y)dy (o)

A: Q5) a)The given integral is, ∫(π2,0)(π2,π2)exsin(y) dx+ excos(y) dy

Q: Find dy/dx without eliminating the parameter. (2n + 1)T A) tan(t) B) 3 sin(t) x = 6 tan(t) – 2, y =…

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Q: Q8// find the general solution (tan-'x + (cotx)y)dx + (lnsinx)dy = 0

A: The differential equation is given as (tan-1x+(cotx)y)dx+(ln sinx)dy=0 Compare it with Mdx+Ndy=0…

Q: Find dy/dx of the following: a. y=sinh-5x b. y=sinh-e* c. y = cosh¹ √√x

A: To find dydx for the given y.

Q: 1.) dx = t (1 + t2) sec?x dt ans: 2x + sin2x = (1+ t?)² + c

A: Since you have posted multiple questions in this question i can do first question as per our company…

Q: 7π| A d) S_T/A (sin x + cos x) dx

A: We will evaluate the given integral in the following step.

Q: Find dy/dx for the following functions:- (1) xlny – ylnx = 1 (2) y = tan-[cosh(2x – 3)] (3) y = (sin…

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Q: 7) Let x = t – sin(t) , y = 1– cos(t). Determine the equation of the line tangent at t = n.

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Q: Q4) Find the derivatives for the following: 1) y? + 3x? – tan-(3x – 12y) = 7n 2) y =…

A: Given,  (1) y2+3x2-tan-13x-12y = 7π    (2) y = sin-1xlntan6x   We have to find the derivative of the…

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.