[0,2m] find ao for f(x)=cos 2° 其bO 2n.c0 0 d O x/2

Q: Given t2 – 1 - f(x) = dt 1+ cos?(t) At what value of x does the local max of f(x) occur?

A: Given that      f(x) = ∫0x[(t2-1)/1+cos2(t)]dt  Here we have to find at which value of x does the…

Q: 1. Find the convolution of f(t) = 3t and g(t) = sin2t?

A:

Q: solve the following x cos?y dx+tany dy = 0 -Q1 y dx = ( x+Vy2-x² ) dy -Q2 (sine - 2r cos?e ) dr +r…

A:

Q: A. For each of the following functions z, find and dx ду 1. z= sin3x cos4y 2. z = tan- 1 (2) 3. yz +…

A: 1). Given: z=sin3xcos4y   As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x…

Q: Given t2 – 4 f(x) = dt 1+ cos2(t) At what value of x does the local max of f(x) occur?

A:

Q: Calculate the approximation for the given function and interval.

A:

Q: One of the followings is a harmonic function O a. u(x,y)=(x' - y' – 2x+1), O b. u(x,y)=(x-y - 2x+1),…

A:

Q: 187. [T] f (x) =1+ cosr, x = 3元 2. COS I,

A: Given: fx=1+cosx The tangent line is to be found at, x=3π2

Q: TL 2 Evaluate the integral: sin(3x)cos(3x)dx 3 1 A B C D H|m 3 16 1 3 16

A: To evaluate the integral. Option c is correct.

Q: find ap for f(x) =cos 2 [0,2n]

A: a0=0

Q: I. Obtain the general solution of the following: D. (3D2 + 12)y = tan x E. (D2 − 3D + 2)y = cos…

A: We have to obtain  general  solution of given differential equation.

Q: Given t2 -9 3 (2)f (=) = / dt 1+ cos (t) At what value of x does the local max of f(2) occur? %3D

A:

Q: find ag for f(x) =cos . [0,2r] 0 a O 2.b0 T.c O 2n d o

A: First option 0 is correct.

Q: c. T(x) = x (**-cos(2x)). find Q at x = t/4. d. T(x) 100e-3x + In(4x), k=470, A= 0.01r and x= 1/3;…

A: c) Given, T(x)=x(x2-cos(2x)) at x=π2

Q: Given t2 – 1 dt 1 + cos²(t) At what value of x does the local max of f(x) occur? f(x): %3D

A: Part 1 of the Fundamental Theorem of Calculus : If  f(x) = ∫axg(t) dt then  f'(x)= g(x)

Q: 2. Find L{f(t)} if f (t) = = cos 4t + t-1/2 + e5t – sin 3t – 5t – 1.

A: We will use the formulas Lcos at = ss2+a2Leat = 1s-aL(sinat) = as2+a2L(tn) = n!sn+1 Hence we have…

Q: The solution to the equation is * y'(x)- 2y'(x)+ y(x)-cos(x) slad Ja sin(x) - y(x) =c,e" +e,xe"…

A:

Q: Given x2 + 11x + 18 f(t) 1+ cos (x) At what value of t does the local max of f(t) occur? t =

A: Solved below

Q: y(x) =- 10 n +2x' +8x' + 48) +qe* +c, sin(x)+ c, cos(x)

A:

Q: Given, f (x, y) = sin (x²y – 2x + 4). Find fy. - x cos (x²y – 2x + 4) x² cos (x²y – 2x + 4) O-x² cos…

A:

Q: Consider the following first-order ODE: (2xy – sec? x)dx + (x² + 2y)dy = 0 || Solve it using the…

A:

Q: Q;: Find for the following functions: - dx xcos (x³+1) 2- y = Tx cos" (x³+1)

A:

Q: Given x2 + 15x + 50 f(e) = 1+ cos?(x) At what value of t does the local max of f(t) occur? 0. t =

A:

Q: ) Given f(x) = t² – 36 dt 1+ cos²(t) Jo At what value of æ does the local max of f(x)|occur? x =|

A:

Q: find the aradients of the functions below a)f(x, y) = e-3y cos4x

A: We have to find

Q: Q3: Given f (x) = sin(x) cos (2x) and h = 0.5, find (numerically): Sf(x)dx а- b- f()(2)

A:

Q: Given t2 - 25 dt 1+ cos2(t) f(r) 0. At what value of I does the local max of f(x) occur? H.

A:

Q: Given: x = 0– sin 0; y = 1– cos 0 d'y Find: dz2 d'y dr? (1-cos 0) CO d²y dr (1-cos e) (1- -cos 0)…

A:

Q: For the given function f(x) = cosx, let xo = 0, %3D X1 = 0.5, and x2 = 0.7. Find the value of…

A: From the given x=0.75, x0=0, x1=0.5 and x2=0.7. It is known that, the lagrange interplotation…

Q: Given ƒ(x) = √²; t² - 25 1 + cos² (t) At what value of a does the local max of f(x) occur? x = dt

A: Ans : x= -5     we use Leibnitz's Rule to solve this problems .

Q: Given x = sin3t, y = -cos3t, then find at t =. %3D dx а. 1 b. 3 с. О d. 2

A: We need to find dy/dx.

Q: 00 | f(x) cos axdx = S2 – a,0 2

A: Value of f(x)

Q: Q: Find for the following functions: - dx 1- y = 2cot2 xcos²(x³+1) 2- y = Tx cos" (x+1) cos²(x³ +1)

A: Simplify the expressions if possible and then find the derivatives. Find the derivatives in the…

Q: T=V3 + cos 0 is given by:

A: Trrr

Q: /2 | cos(r)e sin z dx O a. el O b. e sin 1 C. 1—е 1 O d. cos 1

A:

Q: V3 Find the exact values of s in the interval [0,2x) that satisfy the condition, sin s = -

A:

Q: Solve the D. E. to the I. V. P. sinx(e¬ + 1)x' – cosx = 1, y(곡) = 0 - O (1 + e') (1 + cos x) = -1 O…

A:

Q: Given f(2) = . t2 – 1 dt 1+ cos?(t) At what value of x does the local max of f(x) occur? x =

A: Given the function

Q: Find dy for the following expressions: dx а) y = x5 In(3x) b) у %3D 2 cos + 2x3 3x2 + 7x + cos (x) y…

A:

Q: g(x) - Stoc cos (x + t) g(t) dt = 1 [1- (π/2)]

A:

Q: Given f(x) = , 1+ cos²(t) t? - 9 dt %3D 0. At what value of x does the local max of f(x) occur?

A:

Q: Given G(x, y) = y* sin(2x) + x2(y10- cos(y?))".Find Gyyxxxy- a. - 192 sin(2x) Ob. -192 cos(2x) OC. -…

A: Given:   G(x,y)=y4 sin (2x) + x2 y10-cos (y2)7       ....(1)To find:  Gy y…

Q: evaluate the triple iterated integral.

A:

Q: 4 T/2 a, = f(x)cos(n@,rkdr = "jxcos dx %3D sin 4 cos 2 2

A: Okay I am explaining the marked step.

Q: Given G(x, y) = y* sin(2x)+x² ( x0 º – cos(y²))' find Gyyyxxxy „10 ууххху

A: Consider A(x,y)=y4sin2x and B(x,y)=x2y10-cosy27 then G(x,y)=A(x,y)+B(x,y).Therefore…

Q: -2x 2) (² f(x, y) = e¯ fxx + fyy = 0 Consider -2y cos 2y - e cos 2x. Verify that

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: به)ک ن ان -)f Ssin*(x)cos°(x)dx du )کی + 207 - )J No appropriate Match au)قی - 207 - ه-)J du )کی +…

A: Find the integral match of the integral sin5xcos5x.

Q: Given x² + 13x + • 40 f(t) = 1+ cos2(x) At what value of t does the local max of f(t) occur? rp- t =

A: Here, the given function is: f(t)=∫0tx2+13x+401+cos2xdx

Q: Determine the value of a for which the function F(x,y) equation Fr - aFyy= 0. 8. cos(2x) cos(6y)…

A:

Q: Is this correct?

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.