4. Given f(x)= sin 6x cos 6x dx , what is f| | if f(0)= x ? A. π В. О С. 2л D. — я

Q: 37. ; with r = 1 andh = ;: 0, p2 sin¬! V1-h² /r²-h/r2-n? (0,, 33 47-3/3 (0, 0.71)

A: Let's simplify in steps Let's take the numerator first:

Q: If sin' 0+y cos e sin e cos e and x sin e = y cos 6, prove that x + y* = 1.

A: Solution

Q: Si sin“ (3y) cos® (3y) dy 128 2340135 128 780045 O 9.64 x 10 4 O 2.89 x 10 3

A:

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0, f(x) has a root in [o,. If we use…

A: f(x)=cos(x)-3x+1 secant method iteration formula xn+2=xn-f(xn)⋅xn+1-xnf(xn+1)-f(xn) given x0=0.5,…

Q: If S (x) = - sin(x), then f (11) (x) is equal to – sin(x) B B -cos(x) CosX sin (x) D O cos(x) A,

A:

Q: Solve the diferential egyatien dy - by Melne's méthool with h-o-1 e Cosx dx

A: GIVEN: y'=e-xcosx-y   The formula is: yn+1,p=yn-3+4h32yn-2'-yn-1'+2yn'    ............(1) Put n=3,…

Q: 2.) If H (y) = cos y – sin y, find H (0), H (n),H (T), and also show that H. n+ x) = H (n - x) = -H…

A: The solution is given as

Q: 5 dr dy Suppose x and y are functions of a third variable t. If sin²(x) + cos²(y)=- and dr - 2, what…

A:

Q: d Q 3. Prove that tanx dx sec?x. =

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Q: Suppose that S"(ax + b) cos x dx then the value of a equals

A: Given,           ∫0πax+bcosxdx=6To find: The value of a.

Q: 1 dy sin¬' x If y = xv1 – x² + sin=1 x, prove that 24 – 2

A:

Q: 2. If f"(x) = 4 sin x +16 cos x, f(0) = 6, f'(0) = 1, find f(x) and f ().

A:

Q: s gluai 2 si x = vt +1 ou y = 2xcosx + tanx? as il l J mal (x sec?x? + cosx – x sinx) (1 VE+1 1 (x…

A:

Q: If f(s)=sinh(s)^13 cosh(s)^10 , find f'(s)=???

A: We have  f(s)=sinh13(s)*cosh10(s)   We have to find its derivative…

Q: 3. Why is u = cos x, dv = x dx a poor choice for evaluating | x cos x dx?

A:

Q: 13. For J* sin x dx, what is u? sin x dx 2x dx -x cos x+ 2x sin x+2 cos x +C Oc. OD.

A:

Q: Analyze the approximate value and the exact value for (7.2, 4.02) for the function z = x³y2 sin(xy)…

A: Below given clear explanation .Have a look in hand written solution below

Q: If f cos xdx = A + B sin x + Csin²x+ Dsin³x+ E sin*x+ Fsin5x, what is the value of A + B + CD + E +…

A: Consider ∫cos5x dx =∫cos4x cos x dx =∫(cos2x)2 cos x dx=∫(1-sin2x)2cos x dx…

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); u =

A:

Q: Given that: z = y sin(2x) + (1+x²)e* + cos x tan¬1(y* + 1) In(y6 + 137)

A: z=ysin2x+1+x2ex+cosxtan-1y4+1lny6+137 Differentiating wrt x, we have…

Q: 1 Estimate the error if P3(x) = x - x³/6 is used to approximate the value of sin x at x = 0.1.

A: We have to find the error.

Q: 4) If F(x)= } d, then F'(x)- sin t

A: Note : According To our guidelines we can solve only first question and rest can be reposted.Thank…

Q: •2/3 Find dx. Hint: try either x = 4 sin 0 or u = 16 – x² as a substitution. 16–x²

A: Topic = Integration

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); U =

A:

Q: 5. If z = f(x, y), where x = r cos 0 and r sin 0, find z and and hence show that: (). (-(( 2 2 dz dz…

A: To find the partial derivatives of the following function in two variables by chain rule.

Q: 220. Suppose f(x, y) = x + y, u = ex sin y, x = 1², and y = лt, where x = r cos and y = r sin 0.…

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Q: əz Əz Əx Əy Q5-A) If z =(x +by)² +e+by+sin( ax +by) show that b =a

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Q: Q2// Given that oc= = sec-(-V13/2), find sin x, cos x, tan ox, csc o and cot x.

A: Given: write as Formula used

Q: If S sin 2y cos 2y dy = =, then x is equal to: %3D

A: Hint:    sin2θ=2sinθcosθ

Q: by implicit di f foretiation of sin-(xy) - cos-(x- y) Find -V1- (xy)? xV1-(x- y) ² + V1- (xy)? -V1-…

A: Using Implicit Differentiation

Q: on f(z) = e cos x+ ie-Y sin x is entire.

A:

Q: Suppose f(x, y) = x2 + y? where x = r cos 0 and y = r sin 0. af and Or 1, 0 = 6 Find -when r

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Q: 6. Evaluate |2 Sin xʻdx, by (i) mid-point rule, and (ii) Simpson's 1/3 rule.

A:

Q: Consider the functions h : R→R and g : R -R defined by h(x) = 72 (5 + arctan(sinh 4æ)), . g(x) = 144…

A: Using inverse trigonometric  function properties

Q: Given f(x,y) = e X cos y, Evaluate fx(0,2) cos 2 -sin 2

A:

Q: Given f(x.y) = e X cos y, Evaluate fx(2,0) e2 cos 2 O sin 2

A:

Q: Given that f(x, y) - cos(x²) + 6e* sin y . Find fxyxyx · %3D

A: fx, y=x61+6y-cosx2+6exsiny Partially differentiating with respect to x, we get…

Q: Given f(x,y,z) = cos(5xy) + sin(4z). Find fx(6,6,0). Leave your answer correct to two decimal…

A: Given f(x,y,z) = cos(5xy) + sin(42). Find fx(6,6,0)

Q: There is a unique point a between where the function f(x) = sin x + 2 Cos a and 4 changes its…

A: Given f(x)=sinx+12cos2x Find Concavity  and Find πa

Q: 22: Find dyldx for the following functions * (40 marks) · y = In (3 – 4 cos x) + (4x – 5)5 2. y = x²…

A:

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); i 5 .5 и 3

A: The function is given by  fx, y = sin8x-5y The point is x, y = 5, 8 The unit vector is  u = 35i-45j…

Q: Q4. Given that: z = y sin(2x) + (1+x²)e* + cos x tan-1(y* + 1) In(y6 + 137)

A: Given that, z=y sin2x+1+x2ex+cosx tan-1y4+1 lny6+137 ∂z/∂x is the partial derivative of z with…

Q: (5) Find the local extreme values of the function h(x) = sin?x – V2 . sinx + 2/2 on the interval (0,…

A:

Q: 3. If w-f(x.y) and x-r.cose, y-r.sin6 Prove that - A + fy ar

A: Given that w=f(x,y) and x=rcosθ,y=rsinθ Prove that ∂w∂r2+1r2∂w∂θ2=fx2+fy2

Q: Given f(x,y) = ex cos y, Evaluate fx(0,2) O e² 00 O cos 2 O-sin 2 M

A: We have to find the derivative

Q: a² f For the function ƒ(x,y), compute Or d0 if x =r cos O and x=r sin 0 .

A:

Q: 6. If x= sect and y=tant, evaluate at t =- of the following: dy (a) dx d'y (b) dx?

A: x = sect y = tant

Q: Given that: z = y sin(2x) + (1+x²)e* + cosx tan¬(y* + 1) In(y® + 137)

A: ∂z/∂x  is the partial differentiation of function z with respect to x, keeping other variables…

Q: Is there a value of c that will make sin² 3x f(x) = C, x = 0 continuous at x = 0? Give reasons for…

A:

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.