r' (t) × r" (t) to ||r' (1) × r" (t)|| Use the formula B (1) = T (t) × N (t) to find B (t) , and then check your answer by using the formula B (t) = find B (t) directly fromr (f). r (1) = a cos ti+a sin tj+ct k (a +0, c #0) Enter the vector i as í , the vector j as j, and the vector k as k. B (t) = || ? Edit

Q: d²y If y=cos 4xr, then at x = 0 dx?

A: Given,     y=cos4x

Q: -) Find the general solution of the DE y(4) + 2y" + y = 3 sin t - 5 cos t Use the method of…

A: We can solve this ordinary differential equation by undetermined coefficient

Q: dw Use the Chain Rule to find where w= cos 12x sin 4y, x=5, and y =t". dt dw dt (Type an expression…

A:

Q: dx- B- If y = cos*x – sin*x , prove that: - d²y = -4cos2x dx²

A:

Q: dz b- Solve by chain rule to determine dx z = x²y* -2y , y = sin(x²)

A:

Q: (a) In(1– x) +xe? (b) 2х 2x 1-cos(x) (d) V1+x-1 Check and briefly explain how to avoid the loss of…

A:

Q: e) y = In(cos 4 x) f) y = sin² x y = In(cos(e3*)) g)

A: We can solve using first order differentiation (using chain rule)

Q: A particle moves along the x-axis so that at any time t, t 2 0, its acceleration is a(t) = -4…

A:

Q: Find the slope of the curve 2xy = In(e2*) sin(x) at the point (2,2)

A:

Q: 5*-1 a) If y =Vx* +sin (5x)+ 2 then dy fınd dx b) If y = e2*sinx, then show that d²y =…

A:

Q: Q3.lf f(x,y) = sin²(x-3y)+sin(xy find: and af dy ax

A:

Q: Find the general solution of y′−y=sin x + cos 2x using variety of parameters

A: Given that: y'-y=sinx+cos2x To compare the given differential equation with standard form of…

Q: 1. Lif f(x,y,2)=2exp(-5xyz)cos(15z) Find ôxôz

A:

Q: 1) If y = (x − a)√2ax - x² + a² sin−¹(*—ª),t ), then y'= 2√2ax-x² a is constant.

A: As per instructions, Here is the answer of question 1

Q: dw Use the Chain Rule to find , where w = sin 8x cos 2y, x= and y =t. dt dw dx (Type an expression…

A: Chain rule

Q: d²y Given that y = -4x cos 2x +4 sin 2x, find dx² at x = 2

A: Given: y=-4xcos2x+4xsin2x

Q: y= cos (1-t) and x=V2t - t2

A:

Q: A. Find the function f that satisfies the equation / f(1) dt : 2 cos x + 3x – 5. d B. Evaluate: dx 3…

A:

Q: Q3) A: Find y if: a- y = sin 2x + 2 cos x c- y = sin √x (As... b- y = secx. csc x d- y = tan(2x + 1)

A: Please see the attachment

Q: Find a positive value of k for which y=cos(kt) satisfies y''+25y=0.

A:

Q: 1. If x = e²" and y = sin(3t), find in terms of t.

A: According to Bartleby q&a I can attempt only one question

Q: What is the annihilator for y=x e*cos 2x ?

A: Our Aim is to compute the annihilator for y=x ex cos 2x -(i)

Q: Find the solution for cos(x)" - (1 + x²) – 2xy = with the conditions dx2 1+x2 y(1) = -1, y(2) = 2…

A: Given equation is  cos(x)d2ydx2-(1+x2)dydx-2xy=11+x2 with y(1)=-1 and y(2) = 2 h = 0.25 To solve  -…

Q: The acceleration ā of a particle at any time t is given by à = e-2 î + 3t ĵ+cos t k , then the…

A: The acceleration of a particle is given by a→=e-2t i^ + 3t j^ +cost k^  v(t) = ∫a(t) dt = ∫(e-2t i^…

Q: Can you help me step by step?

A: The derivative of a function is computed as follows.

Q: Determine Yp using undetermined coefficients: 2. (D2-1) y = e-x (2 sin x + 4 cos x)

A: The solution of the problem is given in the next step.

Q: x3 Vx-5 у сos x. sin?x cos3x - Find dy/dx of

A:

Q: Find F

A: Given:

Q: dy 1 dx 3 1 -sin x 3. Find the general solution of +cos(x)y = -e"sinny-². +-cos(x)y 3

A:

Q: 2 S² T ㅠ 1-cos x dx 2

A:

Q: Find d²y/dx² implicitly in terms of x and y. 4xy 5 cos(x) = -9 d²y dx² || X

A:

Q: (b) Find the solution for cos(x)- (1+x?) – 2xy = with the conditions 1+x2 y(1) = -1, y(2) = 2 and h…

A:

Q: y" + 3y' + 2y = e* (t2 + 1) sin(2x) + 3e- cos x + 4e"

A: Answer

Q: 6) x²y" – 3xy' + 5y = 0 ;yı = x² cos(ln x)

A:

Q: Solve the equation for x in terms of y if x is restricted to the given interval.y = 6 - 3 cos x;…

A: The given equation is: y=6-3cosx, and x is restricted to the interval i.e., 0,π.

Q: tan (e) 1+z* (d) (22+ cosh 2z)dz () z coshz dz zp-

A:

Q: 1 = cos t and f(0) = 4 f(0) + f(0+ 2T) + f(0+ 47) ? If f(t) = cos t what is the exact value of %3D 3…

A: ft=cos t and fθ=-14

Q: Find a particular solution by inspection of d²y dx2 +y = -7+e* + cos 2x – 10 sin x

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

Q: y2 Use the modified Euler Method to solve the ODE = dx subject to y = 1 when x = 0 1+x on the…

A:

Q: a) f(x) = 10r23 + el2 + 53 - In(r)+ arccos(x) %3D

A: Given

Q: (b) Determine J cos(x²) 2x dx by using substitution method.

A:

Q: b- y" -y+2y+ cos x, 05x y(0) -0.3, y()--0.1

A: To show the boundary value problem has unique solution we solve the given ode by method of…

Q: 3n 2n n S " S"(sin x + cos y)e? dx dy dz 2n 'n A. 2n(e2n + e3™) в. 2п(е2т — езт) c. 2n(e3™ + e2") D.…

A: Given: I=∫2π3π∫π2π∫0πsinx+cosyezdxdydz   We know that; ∫sinxdx=-cosx+C∫cosxdx=sinx+C∫exdx=ex+C And…

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: (b) Determine cos(x²) 2x dx by using substitution method.

A:

Q: Find the General and Particular solution of = 8 sin 4x ; y= 6 when x = 0 dx Find the General and…

A: The given equations,1.dydx=8 sin4x ; y=6 when x=02. dydx=4y ; y=3 when x=0

Q: Find d2y/dx2 implicitly in terms of x and y 3xy − 4 cos x = −6

A: Find d2y/dx2 implicitly in terms of x and y 3xy − 4 cos x = −6

Q: x2 sin3(x) Q.2\ Find dx if y = In cos(x*).V1+x/

A:

Q: dz 1) Find and simplify in terms of r and using chain rule if given that z=√√4-x²-y², dr x=r cosh…

A:

Q: x² (d) S √1-4x² (HINT: sin² t = dx. (1. (1 - cos 2t).)

A: We have to evaluate ∫x21-4x2 dx.

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.