1 y 21 In(t), t > 0. 2.

Q: (Tlog3(cosh z) + csch x) tanh x dx

A: Here we have to integrate the given Integral

Q: (c) Given tanh (x) + tanh (y) = 1, show that, dy 1- y? dx 1- x2

A:

Q: Determine dy for y=VX2+1 . dx2 alx

A: Obtain the second derivative as follows.

Q: Describe the change in accuracy of dz as an approximation of ∆z as ∆x and ∆y increase.

A: Given , z=fx,yWe do dz using the partial derivates zx & zy .So , dz=zx.dx & zy.dywhere zx…

Q: dy from the equation vx + y = 1 + x'y² dx Evaluate when x =1

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Q: Given that y'= 3y - 100t and y(0) = 10, estimate y(1) using delta t= 0.01.

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Q: dy Find the value of at t = 1 if dx? Vt2 + t, y = t2 + 3 x = 4

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Q: Find the total differential. z = 10x5, y7 dz =

A:

Q: Find the DE by eliminating the arbitrary constant  y = A+ bex

A: Given equation  y=A+be^x Where A & b are arbitrary constant.

Q: dy Given that y = 5u+ 4 and x = -u', hence find dx

A:

Q: Find dy. y=3 In (4+x) dy =D

A:

Q: dæ = -L/R+ x dt

A: Note: It is assumed that R is a constant. Follow the steps below to solve the given differential…

Q: (c) Prove that L{Cost Si(t)- Sint Ci(t)} Logs s +1 %D

A: The complete solution is in given below

Q: dx Evaluate J, +6x+10 by dividing the interval into 8 equal parts by using Trapezoidal rule.

A: The integral ∫15dxx2+6x+10. We have to evaluate this integral by dividing the interval into 8 equal…

Q: (b) Given that y(6x +1) e** = 1+ - In dy Find when x 0 and y=1. dx

A:

Q: 2. f(t) = -3t – 10

A: To find Laplace transform of given function we use the formula of Laplace transform.

Q: 3.) y tanʼxdx +ln* ydy = 0 dy_ (y?+4) Inx In (y?+4)Y 5) dx

A: y tan2x  dx + ln4y dy = 0∫-tan2x  dx =∫ ln4yy dy∫(1 - sec2x) dx  = ∫ t4 dt   (where, t = ln y)Hence,…

Q: Use the Simpson's rule to estimate S, ex dx with n = 4

A: Consider the given integral ∫12ex2dx with n = 4. Simpson's rule is,…

Q: Evaluate: S. yx²dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t?, (0 <t< 1).

A:

Q: Find dy. y = 5 In (5+ x°) dy =

A: If you like the solution then please give it a thumbs up.... The Answer is:           Result :…

Q: 1 dx (25 – x2)3/2 - Show My Work (Required) ?

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Q: ay Differentiate implicitly to find x + y dy dx %3D

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Q: Find the total differential. z = 6x1°y8 dz =

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Q: 22. Find when t=, where x a(t + sint), y= a(I-cost) and a is a constant %3D

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Q: Differentiate.

A:

Q: Let Fes) = fcx-s)dx Find fes) for %3D fex).x^, a constant the funchion where n is

A: Definite integral of the function ∫abf(x)=F(b)-F(a) where F is antiderivative of f .

Q: Find the total differential. z = 10x4y5 dz = (No Response)

A:

Q: dy Find for the following function dv y = In cosh v – tanh? v

A: We have to find dy/dv by using derivative of hyperbolic functions.

Q: (f) y = e* In(tanh(x))

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Q: 1 1+9g2 dæ| dxl

A:

Q: f 5 J of work are needed to stretch a spring 10 cm beyond equilibrium, how much work is required to…

A:

Q: 2. Use the Midpoint Rule with n = 4 to estimate (x² + 1) dx %3D

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Q: Q1: Using Intermediate value to find Y (0.2) dy when = 2x+2y?, h=0.05, y (0) =2 dx

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Q: dy Find for x=secy dx A xsinx B D 1-x?

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Q: Use Leibniz's rule to find 히증 11 Textbook dx for y= 0 S 7x² 8t - dt. 8t+1 Ask my instructor

A:

Q: Find the total differential. z = 10x y10 dz =

A: As we know that the: If the given function is z=fx,y then the expression for the total differential…

Q: Q2) Evaluate , S2 xsiny? dy dx 0 Jx2

A:

Q: Approximate S“ In x dx using three rectangles of equal length and left end points. Is your estimate…

A: The given integral ∫1e2ln x dx, three rectangles and left end points.

Q: Use the Trapezoidal Rule with n = 4 to approximate the value of: +1)dx.

A: Given,  ∫12x3+1dx, n=4

Q: 3 S S t² etu du dt

A:

Q: (b)/ Use the Trapezoidal Rule with n = 4 to estimate ſ,(x3 + 1)dx.

A: To find: ∫-11x3 + 1dx using trapezoidal rule with n=4

Q: With n > 0, does x" dx get larger or smaller as n increases? Explain graphically.

A: Given: The given integral is ∫01xndx. Calculation: Use the integral formula, ∫xndx=xn+1n+1+C.…

Q: Q2. Find of y = 4x/x + V at x = 1? dx

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Q: 2s+3 13. F(s) = s2–5

A:

Q: (c) Given tanh (x)+ tanh¯'(y) =1, show that, dy 1- y? dx 1- x2

A: The given function is: tanh-1(x)+tanh-1(y)=1

Q: Use the Trapezoidal Rule with n = 4 to estimate f, x² dx. Compare the estimate with the exact value.

A:

Q: I = Si S (x² + y³) dy dx.

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.