If y = In(x² + 5) + sinx function then ay at x = 0 is ? dx 11 10 1 10 O 1 O 5

Q: If x= sint and y = cost then 2 dx dy dt dt O 2 O -1 O 1 O O O None of these

A:

Q: i) dt (1+t)3 j) S(sin?x cos x)dx x+3 k) S: -dx x2+6x-11

A:

Q: Let y = tan(4x + 4). Find the differential dy when x = 4 and dæ 0.2 Find the differential dy when x…

A:

Q: f(x.y) =e^sin(y) + In(xy) ; әз of Әхд-у

A: Given: fx,y=exsiny+lnxy To find the partial derivative of ∂3f∂x∂2y Partial differentiation: Partial…

Q: dy evaluate dx (sinx+1) 5-1f: y = (cosr+1)

A:

Q: Let y = tan(5x + 4). Find the differential dy when x = 5 and dæ = 0.4 Find the differential dy when…

A:

Q: 1 Let y = -. Find dy and Ay at x = 7 with dx = Ax = – 1. Enter the exact answers. dy = Ay =

A:

Q: d²y if dx2 sinx O Find Lon Vt2 + 5 dt + sinx = y- x secx

A:

Q: dy at t= T is dx If x=t+sin 2t , y = 3t – cos 2t, then O a. -1 O b. 1 O C. -2 O d. 2

A:

Q: *show work*

A: Find dy/dx.

Q: dy соmpute dx for implicitly given function cos(xy) + 2y = x³

A: cos(xy)+2y=x3Differentiate with respect to x,-(sin(xy))y+xddx(y)+2ddxy=3x2

Q: (e* + In y + ) dx + ; 10. + Inx + sin dy = 0 Answer: e* +x In y + y ln x – cos y = C

A:

Q: π Q3/ Evaluate Sosyx siny dx dy 0 0

A: Consider the given integral, I=∫0π∫0cosyxsinydxdy perform the integration,…

Q: If y= sin f dt, then dy is dx 2x sin x sin x 2 VX sinx 2x sinx

A:

Q: dy Find the particular solution of 2y- = x+ sin a when y (0) = 1

A: we have to integrate both side , we get

Q: SOLVE THE FIRST ORDER DE. dy – yln(yecosx)dx = y sinx dx

A: dy-yln(yecosx)dx=ysinxdx

Q: If y = f(x) is the solution of (-x – 9)dx + (x2 + 10x + 41)dy = 0, f(0) = }In(41) +arctan(5/4), then

A:

Q: t F(x) cos(3t – 1) dt sin z %3D

A:

Q: Find dy/dx for the following function:- (1) y= In(r+4)-xtan (4) y x*+1) (2) xy +xy x+ 3y (3) Iny e…

A:

Q: Q2: Find dy/dx for the following function: (1) y = In(r + 4) -x tan (4) y = x+1) (2) xy +xy = x+ 3y…

A:

Q: Let y = 5x?. Find the change in y, Ay when a = 3 and Ax = 0.3 Find the differential dy when x = 3…

A:

Q: Q1) Lind dy/dx of O xe 1o X +3y = 0 2 2sinx cosy=1 9 x = sec!

A: As per our company guidelines we are supposed to answer only one question kindly post other question…

Q: dw "(1),y = sin (1),-: 2) w=+ x= cos at =3 Ans. -1 dt

A:

Q: COS f(2, Y) af af dy f(x, y) = log, (3x) af %3D fe dy

A:

Q: 1)Find dy/dx for following functions. 1) y = (In 4)* + In () (Inx)2+ (In Vx)3 3* 2) y = tan-1 (x*)

A:

Q: (a) Find the differential dy. y = cos(x)

A: Differentiate the given function with respect to 'x' and find 'dy'.

Q: B. Find y). 1. y = cosh?x 2. y = x tan-1 x - In vx2 + 1

A:

Q: If f(x,v) = ex In(5xy) find dy?

A: Given: fx,y=ex2ln5xy. To find: ∂2f∂y2 Solution: In partial derivative we differentiate with respect…

Q: dy of the following functions: dx b) Find the y = sin V1+ Vx y= In(In(tan.x)) i. ii. Vx + Vy = 4 at…

A: b. (ii)

Q: 17. Let y = 4t + 3, t = 6e and s = 1 + In x. Find dy in terms of x. dx %3D

A:

Q: d cosh z =sinh x dz صواب ihi

A: Use the formula of coshz and sinhz in terms of exponents.

Q: Find the general antiderivative of the given function. f(x)= sin (7y)+ cos (3y)

A:

Q: II. Find dy/dx of the following functions: 1. y = cosh √√4x²+3 2. y= sec hx² x² +1 3. y=xcsche4x

A: See this solution in below

Q: dy for y=In (x² +1}+ (sin x +5)*. Find dx

A:

Q: 2. f" S"(sinx + cosy) dx dy

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: 2. F(x) = fr Cos t dt %3D

A:

Q: 7. Calculate dy/dx at the point indicated: f(0) = (7tan O, cos O), 0=/4

A: Here we will use the concept of parametric equation and Derivative of parametric ewyations

Q: dx dy Suppose x and y are functions of a third variable t. If sin²(x)+cos²(y) =- and dt 1, what is…

A:

Q: dy Given y³ In x + x¹e³y = sin-¹(xy), compute da

A:

Q: Find the value(s) of at y= 1 given that x2y+y2 = 5. dx

A:

Q: dy A: Compute dx at the point (1, 0) for the function y = cot-1(4x + eln(sin2x)) + sinh(3) + log2 x²…

A:

Q: Q3: Find if: dx 2x dt sinx dt (1) y = (2) y = [ %3D t- 2 X cosx

A:

Q: Let y = tan(4r + 4). Find the differential dy when x = 1 and dæ 0.4 Find the differential dy when x…

A: Given that, y=tan4x+4 differentiating both sides with respect to x, we get…

Q: The linear approximation at x = 0 to sin(4x) is A + Bx where A is: and where B is:

A:

Q: dy at x=0. dx If y = (3x² + 4x + 5)(e* – cos 2x), then find %3D -

A:

Q: 10 cos(x) Evaluate the improper integral: / dx Vsin(x) а) 30 b) O20 40 c) 3 d) Odiverges e) 10

A:

Q: If x = 3 sin* t and y = 2 cos" t , then find dy at t = dx 4

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.