Where a is a constant, then a is equal to:

Q: If f f(x) da = –34 and F(17) = –45, where F(x) is an antiderivative of f(x), find F(3)

A: Given : ∫317fxdx = -34F17 = -45

Q: If g(s,t) = f(s^2 - t^2, t^2 - s^2) and f is differentiable, show that t(∂g/∂s) + s(∂g/∂t) = 0

A:

Q: cln 3 Evaluate f" sech² t dt 15. B. ? c. A. D.

A: From the given problem: I=∫0ln3sech2tdt As we know that: ∫sech2(x)dx=tanh(x) And…

Q: Any two antiderivatives of f (x) differ by a constant.

A: We need to check whether two antiderivative of f(x) differ by a constant.

Q: functions

A: We have to find the antiderivative of the given function according to the given information

Q: Consider f (x, y) = log(r² + y²) f.(x, y) = %3D and fy(1,0) = %3D

A:

Q: Let f(x.y) = 3xy + x?y. Find ,and dxdy' дудк dy

A: We have to find given differentiation.

Q: Find L[f (t)] where f(t) = eat and a = constant

A: Solve using Laplace transferom

Q: L{f(t – a)u(t – a)} = e¬as F(s) |

A: Topic:- Laplace transform and it's properties

Q: Find the convolution f (t ) *g(t) f(t)=e^at,g(t)=e^bt

A: By definition of convolution, we have

Q: "+ Ri = E, where L, R, and E are constants whent = 0, i = 0 dt

A: Linear differential equation in standard form is given as: dydx+py=q where p and q are function of…

Q: So, which of the following is the solution functiony(t) ? a) y(t)= sinh2t = e* %3D b) y(t) = sin2t –…

A:

Q: Find the antiderivative of f(x) = 2 csc2 a given that f () = 1. 4.

A:

Q: Use Part 2 of the Fundamental Theorem of Calculus and the following formula to find the derivative.…

A: The given formula is  ddx∫ag(x)f(t) dt=f(g(x))g'(x) We have to find the value of  ddx∫2sin…

Q: Let f(x, y) = y log (xy). Find: (г, у) fyr (x, y)

A: We have to find the partial differential fyy and fyx.

Q: Find the most general antiderivative F(r) of the function f(x) in each part: a) f(r) = 12r3 +4VT- e…

A: To evaluate antiderivative F(x) of the function f(x)=12x5+4x-ex+1 We know that∫xndx =xn+1n+1 +C ;…

Q: Suppose z is a function of x and y, and csc Vx2 + yz = 2"esin . Solve for dz and ду

A:

Q: Evaluate and simplify y'. In x where a is constant y In x + a

A: Given:   y=lnxlnx+a

Q: the constant 'c' such tha 5y)âz + (y – 3x)ây z)âz

A:

Q: Find the general antiderivative of f(x) = 4x – 5. Use Cfor the arbitrary constant. nswer F(x) =

A: Fx=∫fxdx

Q: The function e is an integrating factor for the ODE y' – 2xy = x7 %3D True False

A:

Q: Which of the following function/s is/are homogeneous? d) 1/ (2√x+y) e) ln(x-y) f) x/ (√x2-y)

A:

Q: Find the d. c. of from definition. Vx

A: As per the question we have to find the derivative of the function : f(x) = 1/√x Using the limit…

Q: Differentiate g(N) = rN g'(N)= with respect to N. Assume that K and r are positive constants.

A: We need to find g'(N).

Q: d?y taby = Fo cos ot, where wo, ware positive con- dt- stants, and Fo is an arbitrary constant. You…

A: Given differential equation, d2ydt2+ω02y=F0cosωt      ...(1)

Q: Express the statement as a formula that involves the given variables and a constant of…

A:

Q: ,use the linearity of L   determine L[f]. Q. f(t)=cosh bt, where b is constant

A: Given,

Q: Given f(x) below, find f'(x). f(x) = z" t' dt √z

A: See this solution in below

Q: If y=e"Inx, show that x (1+x)=0. dr

A: Given: y=e−x.lnxShow  that:x2d2ydx2+dydx+e−x(1+x)=0

Q: If f(x)dx = 32, then f(t)dt : %3|

A: Here, Order of limit has been exchanged with each other.

Q: given f (z) = (z + 1)° – 32' what is the value of u (금, )

A: Topic:- complex number

Q: Use the Fundamental Theorem of Calculus Part I: d 10. dx J14 n(t + 3)dt

A:

Q: valuate |v(t)dt 1

A: We have given a graph in which the velocity v(t) of an object moving along a line is given where…

Q: f (x) = sec? x +1

A:

Q: Determine all values z ∈ C satisfying  e^z = −2i.

A: ANSWER :

Q: Given g(z) = In(5z+), the derivative g (z) is. %3D O 42 O 5z +z O 20z +1 O 20z +1 5z4 +z 5z +I 20z+1

A:

Q: Find the antiderivative F(x) that satisfies the given condition. F'(x) = 4ex - 5x²; F(0) = 10

A:

Q: Given that f(x) = sin a cos' r +2 (sin r + a)' +, the value of the constant and the least value of f…

A:

Q: Let f (x, y) = csc(x + y³) ey , find дудх

A: The given function is  f(x,y)=csc(x+y3)exy. The main objective is to evaluate ∂2f∂y∂x.

Q: Given a function f(w, x, y, z) = 2(w + 1)² x − xe²+, which of the following is not part of the total…

A: Given a function fw, x, y, z=2w+12x-xez+y2zw, to determine which of the following is not part of the…

Q: Find an antiderivative of f(x) 28. Assume that the value of the arbitrary constant is 0. Answer

A: Antiderivative of function

Q: The function e is an integrating factor for the ODE y' – 2xy = x7 - True False

A:

Q: (b) If g(x) = [,! 1 dt, find g'(x) 4+t2

A:

Q: Given f(t) = e*t, what is L{t?f(t)}?

A: The Laplace transformation of a function f(t) is given by the equation; Lf(t)=∫0∞e-stf(t)dt=F(s)

Q: This function f(x + iy) = (x2 +x - y²) + i(2xy + y) is differentiable ? False O True

A:

Q: If A = f+g,+ h s.t f(x.y.z) = e2, g(x.y.z) = xcosy, h(x. y.z) = log 2z then div A

A: Identify the coordinates system. Then use divergence formula.

Q: -)-= 0 ,y'at y = a (b is constant)

A:

Q: then the integrating factor is (a) x* (b) (c) Inx4 (d) x*

A:

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.