Solve the following problems. Write the correct unit and box your final answer. Topic: Applications of Differentiation (Calculus 1) Find the particular solution to the differential equation d'y 2 dx = 4e* + 3x given y = -3 and y = 3 when x = 0. dx

Q: Find the first derivative of y = ( ex – e –x ) / (ex + e –x ) and y = ln [ x + √ (x2 + 1) ]…

A: y = ex-e-xex+e-x,Differentiate w.r.t.'x'Apply the Quotient…

Q: 1. Solve the equation: (4D4 – 4D³ – 23D² + 12D + 36) y = 0 O y = cje* + c2xe2" + c3e¯7 + c4xe¯i O y…

A: The given equation is: (4D4-4D3-23D2+12D+36)y=0...(1)

Q: Sketch the graph of f(x) = 2x + Vx*.

A: Given that we need to Sketch the grah of  y = 2x1/3 + x4/3  Now,  The graph is as follows

Q: Evaluate the integral Se*dx

A: We can solve this as follows:

Q: x² – 3x – 7 - dx (x² + x + 2)(2x – 1)

A:

Q: II. Consider the function g defined by 1 g(x, y) = cos (Tx Vy) + log3(x – y)" Do as indicated. 1.…

A:

Q: and

A:

Q: Convert to a polar coordinates. 13. (0,–4)

A:

Q: Find the derivative of y = sin x³ cos x?

A: As per our  guidelines we are supposed to answer only one question. Kindly repost  others  questions…

Q: 11. Prove that tanh y du = In cosh u + C

A: The integration of the integral is tanhu.

Q: 1) Find the Taylor series for f(x) = In x centered at 3. Show All Your Work.

A:

Q: Solve fo x: 3csc(x) + 2=0

A:

Q: 4. csc 2x lx

A: The integration of the integral is csc3(2x).

Q: 3. (a) Calculate sinh (log(5) – log(4)) exactly, i.e. without using a calculator. Answer:

A: Solution is given below:

Q: 5. Solve the equation: (D² – 3D + 2) y = 2x² + 1 O y = cje + cze² + 4x + 3x2 + x O y = cje* + cze2x…

A:

Q: Find f'(x). Given: f (x) = 5xv3x² – 4

A:

Q: 4. (a) (i) Calculate (4 + 10i)?. Answer:

A:

Q: Find the function F(x) such that F' (x) = 8x and F(0) = 1 O 1+4x^2 O 4x^2

A:

Q: L(e3t cos 2t)

A: We know, L{eatf(t)}= F(s-a) , where F(s)= L{f(t)} L{cosat}=s/(s²+a²)

Q: 2

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Q: 2x²+x² x dx

A:

Q: Supply the missing integrand and limits of integration. dy (3x² – 2xy + y³) dx dy

A:

Q: For the first 10 days in December a plant cell grew in such a way that t days after December 1 the…

A: use derivative  to evaluate the volume

Q: Find the dy/dx: Given 2x x+1 y =

A:

Q: What is the range of the inverse sine function y= sin- (x)? (-골, 글) A 2 2 B ( 0, π) 2'2 D [0, 1]

A:

Q: 13. Evaluate: sin(x²) dx A) 2x cos(x2) B) 2x sin(x?) C) 2x cos 2x D)2x cos x 14. Find the derivative…

A: To find Evaluate the integral:

Q: The volume generated when the region bounded by y = x , y = 1, x = 0 is rotated about x - axis is…

A:

Q: x + 4 dx x² + 2x + 5

A: Given ∫x+4x2+2x+5dxTo evaluate the integral:

Q: dx 6. J Vx2-4x+13

A:

Q: TRUE OR FALSE 10. Addition and Simplification can be applied to part of lines of proof. 11. If p, q,…

A: Here is the solution

Q: EVALUATE THE FOLLOWING cot x dx 4 sınx + csC X 1.

A: A detailed solution is given below

Q: Use Integration by Algebraic Substitution 3 dx x +1

A:

Q: What is the definite integral representing the area of the given region below? A. A= (1,1) В. А-D…

A: Area of a region bounded by two curves y=f(x) and y=g(x) is given by, A=∫ab |f(x)-g(x)|dx where a,b…

Q: What is the range of the tangent function y=tan(x)? A R B [- 1, 1 [0, + ) D (- 00, 1]U[1,+ ∞)

A: Tanx is the ratio of sinx and Cosx

Q: | In (x²- 2x-8) dx 5. ら

A: Explanation of the answer is as follows

Q: II. Evaluate each of the following limits. 1-V3-x 4) lim x→2 4-x2 5) lim x→∞ 3 Sin ) 2 6) lim(4x +…

A: We have to evaluate the given limit.

Q: Evaluate the given integrals. 1. ſ cos v2x dx 2. fx a*dx

A: Please see the answer below.

Q: Determine whether the Mean Value Theorem can be applied tof on the closed interval [a, b]. (Select…

A: Given function  f(x) = x /(x - 25)          Let's check mean value theorem.

Q: 9. The general solution of y" + y = cos? x

A: Given :   y"+y=cos2x

Q: (a) Find the equation of the tangent line at A. (b) Find the area of the shaded region enclosed by…

A:

Q: Experimental data on the nitrogen content of soil samples taken from a field used for vegetation was…

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Q: F(s) = (s-2)(s-4)(s-8)

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Q: 2r³ – 4x² – x – 3 dr x² – 2x – 3 in |x + 1|+ 3 1n|x – 3| + C in |x + 1| – 3 In|x – 3| + C Option 1…

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Q: wen F(x) below, find F'(x). F(x) = dt I+8 rovide your answer below: F(x)-D I FEEDBACK MORE INSTRUCTI

A: Topic:- function And it's integration

Q: Use linear approximation to approximate e.03 О 1.03

A:

Q: 2. Solve the equation: y" – y " -2y' = 0 O y = cje* + c2 + cze2* O y = cje* + c2e* + c3e2*

A: The given equation is  y'''-y''-2y'=0

Q: 3. Find the reference angle (also called the reference number) for the angle: 13n radians. 11

A:

Q: 12. Solve 2cos²(20) = 1. List the solutions that are: 0 < 0 <n %3D

A: Here, the given equation is: 2cos2(2θ)=1⇒cos2(2θ)=12⇒cos(2θ)=12 or cos(2θ)=-12

Q: Q1: Find The Fourier series for the function defined by 0 <x < 41 -4 <x< 0J f(x) = {* - %

A:

Q: 2

A: Here we can see as t approaching to 12 , graph is approaching towards 150.