6) x*dx_ .2 S2x-x

Q: (In x)* Integrate: 1

A: Given,            ∫1eln x4xdx

Q: 5 Find a limit equal to In(2x – 1) dx.

A: We know that, ∫lnxdx=xlnx-x+C…

Q: (5) Evaluate the definite intergral [/³ (sec²x+3x)dx. /3

A:

Q: 4. Give an example and a proof to not increase intrinsic distance.

A: We have given statement that Local isometries can shrink but not increase intrinsic distance. We…

Q: 4. Evaluate the integral. S tan (2x) sec°(2x) dx

A:

Q: x³dx S 17. √(1-x²

A:

Q: tion, what is the longest time within whic at the predator will have to spend more t

A: It is found that the time (in minutes) required by predator to find a prey is a random variable that…

Q: Compute 3 In(x² + 1)dx=

A:

Q: 5. Show that dS = 0. lav

A: The objective is to show that, ∮∂VdS=0. Let V=cT where c is a constant vector. Now by divergence…

Q: Prove: cosh 3x = 4cosh'x- 3 cosh x %3D

A: We will solve the following.

Q: Compute integral23  3x^2+2x+1 / x^2 dx

A:

Q: Consider the indefinite integral *7x³ + 9x² + 12x + 24 -dx x4 + 4x2

A: Given,            ∫7x3+9x2+12x+24x4+4x2To find : The partial fractions decomposition.

Q: EXAMPLE 4 Use the Table of Integrals to find SxVx² + 4x + 11dx.

A:

Q: evaulate the indefinite integral  4x^3+2x^2+6x-5/(x^4-x^3)

A: Firstly, We factorize the denominator

Q: Compute integral-11  3x -√1-x^2  dx

A:

Q: 3. Prove that cosh (2x) = cosh²x + sinh²x %3D

A:

Q: Compute integral23   3x^2+2x+1/x^2  dx

A: The given integral is ∫233x2+2x+1x2dx.

Q: Use (3) from Section 5.4 to evaluate the integral. '5 dy

A: We have to find given integral.

Q: 6. Prove that 1 cosh(tanhx) : -1 <x < 1. V1- 12

A:

Q: 3. Prove that coshx – coshy = 2sinh () sinh ().

A: As per honor code we are entitled to solve only 1 question at a time so I am providing you the same.…

Q: 5. Compute Jo Jitvx 1 dx -2

A:

Q: 4. Find at the point (1,1,1) if ln(xyz) = 1 əx

A:

Q: Find upper and lower bounds for

A:

Q: Compute.  integral (x) / square root(3-2x-x2) dx.

A:

Q: Prove: cosh 3x = 4 cosh° x x-3cosh.x

A: Prove that :- cosh 3x=4cosh3 x-3cosh x

Q: Evaluate: 2) x-In x dx

A:

Q: 4х, th dt Vhat is the

A:

Q: State Green’s Theorem

A:

Q: If Z= sinh () x- show that:

A:

Q: Compute. integral x2arctanx dx.

A: It's a integral question so I'm provided hand written solution.

Q: Find y' by ased proportici Ln Xャ3

A: Taking natural log both side

Q: (5) Find the integrals: •ftan²(x) dx ● fsec²(x) dx • ftan³(x) dx ●

A:

Q: 9 In(z² – 1) dz

A: Given: ∫9lnx2-1dx

Q: Compute ∫xsin(3x−2)dx.

A: Let the given

Q: Show that L₁J - dx x² + 2x + 2 = In(√5-2).

A:

Q: 9. tan 4x sec24xdx d. cos 5xsin 5xdx e. x sin(3x² +1)dx f. [x* cos(2x' +1)dx

A:

Q: у %3DIn(In sec x)

A:

Q: 2. Use Theorem 4 to evaluate (3x +2x2) dx

A: Given ∫01 (3x+2x2)We know that ∫xn=xn+1n+1+C

Q: 4. You will need to use L'Hopitals Rule in this one Sxe-* dx

A: This is a improper integral problem

Q: 15. -- sin(2+ 2) dz

A: According to the given information, it is required to solve the give integral.

Q: 6(2tanx - x^4 + 4lnx)^1/4(2sec^2x - 4x^3 +4/x)dx. Hint: let u = 2 tanx - x^4 + 4lnx

A:

Q: 1. Express into parital fraction. Hence evaluate y2 -4 *2-4

A: according to our guidelines we can answer only three subparts, or question and rest can be…

Q: Evaluate the integral. S sin (7x - 10) dx ㅇ cos (7x-10) +C -cos (7x - 10) + C cos (7x - 10) + C 7…

A:

Q: if X #0 メ=ロ Frnd continuous

A: given the function fx=xx if x≠00   if x=0 we know that x=x if x&gt;0x=-x if x&lt;0 therefore,…

Q: Compute. integral 1 / square root(-x2 + 4x) dx.

A:

Q: 7. Find the first 2 iterations for the root of f(x) = x- cosx by the Secant method on [0,1.

A:

Q: 1 Integrate: S tan*÷x dx 3

A:

Q: If g(x) : 8 + cosh(9x) find g'(x) 8+ cosh(0)

A: Answer and explanation is given below

Q: evaluate Inteyral 2 2x-1 x3+x2

A: The given integral is ∫124x2+2x-1x3+x2dx. Calculation: Rewrite the partial fraction of the integral…

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.