1. Plot the function f(t) = 5 sin(x) x+e-0.75x 5 3x for -5 sxs 10. Make two separate plots of the function f(x) = (x+ 1)(x- 2)(2x - 0.25) - e, 2. one plot for 0sx<3 and one for -3sx56.

Q: 0,-T <x<0 tsen x, 0sx < T 9. f(x) =

A:

Q: Q4: Find an equation for the line tangent to the curve 2y cos x = 4x sin y , at the point where x…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: y-(x-5)2 + Sin-l XY 4.

A: To expand: y-(x-5)2+sin-1xyx+5.

Q: 38. A. -arcsin x x Vx2 – a² 39. 1 В. -arccos x a2 + x2 40. 1 С. | -arccot x Va? – x2 - D. -arccs x…

A: Match the following

Q: 4 b. [√x ln xdx, 1 4 ㅠ C. fx√4-xdx, d. fx sin (2x) dx. 0

A: Solve the following

Q: 1) f(t) = e3t+ sin²t +6 cosh /7t -3t²

A: We'll answer the first question since the exact one wasn't specified.  Please submit a new question…

Q: 5 dx Find dx, x> V25x? -9 5x In 25x2-9 + C 3. sin-13x+c 1+9x2 +3x|+c 1 V1+9x? + C 3x 3. + C V25x2 -9…

A: The solution is given below in the next step:

Q: 4 - Find the direction A in which the function f(x, y) = x cos y + y sin x decreases most rapidly at…

A: We have to find the direction A in which the given function decreases most rapidly.

Q: Q5: Find for the following functions: dx (4) y = x sinh 2x-cosh 2x (3) y = e* sin² x In√x

A: See this solution in below

Q: dy 1- Find by implicit differentiation. dx 2- x2 + y2 = 100. 3- x3 + y3 = 3xy². 4- x²y + 3xy3 – x =…

A:

Q: c. Let y = x-5 – 3 ln () – d³y a x3 (or) y(3) -7 sin 3x. Find

A: Explanation of the answer is as follows

Q: 1 y = x²-1 Using differential, draw the function

A: This is a problem related to differentiation. Based on the general formula and concept we will…

Q: X(t) = b cos(wt) + V a² – b² sin²(wt)

A: We will use differentiation rules to solve this question.

Q: 4. Differentiate the following function.   y=5e x−5x dy/dx=nothing   Enter your answer in the…

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: Find the length of the graph of ; a. f(x)=⅓x2 -⅔ between x=2 and x=3.  b. x=cost, y=sint from t=0…

A: See the detailed solution below.

Q: Find the linearization of the function y = f(x) = x2 sin(x) at a = π/4 and use it to approximate the…

A: Given,

Q: B) Find for the Implicit function: dx x2 - sin(xy) + y² = 5xy

A:

Q: y³x2 + yx³ - 20y² – 10y = 0 sin(x?) = cos(y³)

A:

Q: (1) f(x, y) = e-(r²t;2 ) (2) f(x) = (x – sin(x))2

A: Note: "Since you have posted multiple question. As per our guidelines we are supposed to solve only…

Q: 4) a) Determine the derivative dx of the following functions y = 3** b) 1-3- 3e² 1² c) y d) y =…

A: We have to find the derivative.

Q: Determine the most appropriate method to find the general solution for the functions: y" - y' - 2y =…

A: Given differential equation is y''−y'−2y=2x+sin2x−4hcos2x. We have to determine the most appropriate…

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: Q5: Find for the following functions: (4) y = x sinh 2x cosh 2x (3) y = e* sin² x In√x

A: The given functions,3) y=exsin2xlnx4) y=xsinh2x-12cosh2x

Q: ) S² e2x sin x dx T/2

A: To find the integration from 0 to π/2 e2xsinxdx

Q: – 2x 4. Find the first five derivatives of y = Sin 3x+ e¯2x + In 7x. %3D

A: Our Aim is to calculate the first five derivative of function given below:-y= sin(3x)+e-2x+ln(7x)…

Q: 2. Y=12-36x, Y'co) = 5, 2. dx and yeo) =S. YCx) =?

A:

Q: Find F

A: Given:

Q: determine the annihilator of the given function. Q. F(x)=17e3x sinx

A: The given function is  F(x)=17e3x sinx. It is of the form , xn-1eαx sinβx. n=1 , α=3 , β=1. The…

Q: Q1)Find dy/dx for the implicitly defined relation sin(xy^2)=xarctan(y). Q2) Find the first two…

A: Given:sin(xy2)=xarctan(y)Differentiate both sides:cos(xy2)y2+2xyddx(y)=arctan(y)+xddx(y)y2+1Isolate…

Q: f sinh3³ x dx Ocosh³z-coshz+C O3 cosh³r+C 3 Ocosh³z + cosh 2+ C Ocosh³ +C O None of the choices

A:

Q: b) y" + y' = sin 2x

A: here we need to find the particular solution of given differential equation. the solution is…

Q: 50. g(x) 52. f(x) = xe* 54. y = sin²(e³x+!) %3D

A:

Q: h(x) = x – sin x for 0 <x < 4A -

A: Given the h(x)=x-sinx for 0≤x≤4π We need to determine: a)the intervals of monotonicity for the given…

Q: 1) Find the Linearization x of the function -V1+2x when x is near 0 Find the equation of the tangent…

A: As per Bartleby guideline if more than one question is asked only first question to be answered…

Q: Solve for the particular solution of the ODE y" + 4y' + 3y = sin(e^x).

A:

Q: dx 4+5 cos dx sin x + cos x+3 dx (solve in two ways: let x= x² Vx² + 1

A: To integrate:∫dx4+5cosx. Solution: ∫dx4+5cosx We know, cosx=1-tan2(x2)1+tan2(x2) Substituting above…

Q: 2 S tan x sec x dx e-0.3x =27 Q5) (A) Evaluate (B) Solve for x: |3D

A:

Q: 4. a) Find the following derivatives using differentiation rules. d dx 5 2)* d ii) Vx + dx d²y b) If…

A: 4 First we will see differentiation rules.…

Q: Find the antiderivative of the function f(x) = - 4 sin (4x) when C = 0. The antiderivative is

A:

Q: Q2) Find the derivative of the function at Po in the directi g(x, y) = x – (y²/x) + V3 sec-' (2xy),…

A:

Q: 3.9.27 Find the derivative of y with respect to x. y = sec 1(5x2 + 1). -1(5x2 +1), x > 0 dy %3D dx…

A: Please see the answer in Step 2

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: Find the actual error when the first derivative of f(x) = sin(2x) at *=1/8 s approximated by the…

A:

Q: Can you help me with this problem step by step?

A: Differentiating implicitly with respect to x on both sides. Solving left hand side first.

Q: b. Find first and second derivatives (dY/ dX, d'Y / dX² )of the following functions aX² +1 (а) Ү -…

A: The given problem is to find the first and second derivatives of the given following functions.

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

A: We have to evaluate ∫x21-4x2 dx.

Q: Please solve the Vƒ of the function below at point P. a) f = (x² + y² + 2)-05, P; (12,0, 16) b) f =…

A: a) The given function is f=x2+y2+z2-0.5. This gives ∂f∂x=-0.5 x2+y2+z2-0.5-1…