Consider the function Z = 2x2 (1 – e-y) where x and y are given to be 6 and ln 6 respectively. Find the absolute change AZ in Z if Ax = 0.1 and Ay = 0.03. 2.84 O 3.16 O 2.04 O 2.36

Q: d In (t2 + 1) dt = dx A) In(x6 + 1) B 3a In (a? + 1) 3x ln (a6 + 1) In (x® + 1) In (e? D -

A:

Q: dy 24// A- If y= cosh(t³ – 1)+ log2(3t + 1)10 - In (sin-1(e-t)), find dt B- Find a value of n so…

A: In the A part of the given question we have to find the derivative of the given function…

Q: Find the following definite or indefinite integrals: 2+In x dx a) S-

A:

Q: Solve the following ODE by introducing integrating factor on the process of your calculation: x…

A: Given differential equation.x dydx2x+1x+1 y=x-1Comparing with the standard form.   dydx+Px y=Qx…

Q: 20. Evaluate.d(x³ sinh(Inx)) O a. 2x3 − x O b. 2x² O C. 4x²-x O d. 2x2 − x

A:

Q: 2. Evaluate the following: S y(x² + y²) dxdy a. e2x+sin x-1 b. lim x-0 log(1+6x)

A: We have to find the following double integral

Q: 1) Find dy/dt for if : y = log2 (81ln 2) 2) Evaluate the following integral: In 2 " log2 (x + 2)* dx…

A:

Q: Complex analysis

A:

Q: e ax dx

A: 1. Let In=∫xneaxdx. Use the integration by parts formula ∫udv=uv-∫vdudxdx to evaluate the integral…

Q: 1) Find dy/dt for if : y = log2 (81n 2) 2) Evaluate the following integral= In 2 log2 (x + 2) dx x +…

A: Any logarithmic function having a base other than e can b converted to a natural log as shown below:…

Q: ) Evaluate the following integrals 1) L 8(T – t) (T + 4) dT dt 2) Ltu(t – 1) u(4 – t) dt 3) S 8(x +…

A: (3) ∫0∞δ(x+2)e-x dxI=∫0∞δ(x+2)e-x dxx+2=0x=-2 I=e-x∫0∞δ(x+2) dxI=0   {because x=-2 lies outside the…

Q: For the discrete logistic equation xt + 1 = Cxt(1 – Xt) and the given values of xo and c, calculate…

A: Let's find.

Q: 3) Show that for any constants M, k, and a, the function (",) A(1 - ) y(t) 1 ·M|1+tanh ´k(t – a)…

A:

Q: If f(x, y) = e®¤ . In(16y), then fræ is given by: O 144 e9 In(16y) O - 81 e9 ln(16y) O 81 e9 In(16y)…

A:

Q: Q16: Compute the following indefinite integral xʻe*dx

A: Please find the solution of questions.

Q: Evaluate the integral. (x² + 2)e¬× dx

A: To evaluate:∫01x2+2e-xdx

Q: Evaluate the definite integral. 2 e 1/x* dx x

A:

Q: Q16: Find the indefinite integral: (e' + tº) dt

A:

Q: Use mathematical induction to prove that the n-th derivative of (x +n + 1)e" is given by d" (x+1)e =…

A: We use mathematical induction. The detailed solution is typesetted and given in detailed as the next…

Q: Let f(x) = 16 ln( – x) + 4x + 13. (a) f'(x) = (b) Solve f'(x) = 0 to determine the critical values…

A:

Q: Determine how large the number a has to be so that 1 dx

A: We have to find out the value of a .

Q: Find the indefinite integral. ∫(e1t/t2) dt

A: Given: I=∫e1tt2dt for evaluating given integral, in given integral we substitute  1t=p…

Q: Which of the following integrals will NOT result into a natural logarithmic function? 5x xp: sec x2…

A: Evaluate each integral separately.

Q: Find formulas for the functions represented by the integrals.

A: Find formula for the function represented by the given integral: ∫1x2 t dt

Q: b) Calculate the following definite integral: [*(√x - 3) dx

A:

Q: Find the linear approximation of f (x) = ln e at L() In(1.42) 1 and use it to estimate ln(1.42)…

A: Given function is f(x) = ln x and the linear approximation is to be calculated at x = 1.Linear…

Q: 1)Differentiate the following f(x) = x³In (3x² – 2x + 7) e sin (x) g(x) = %3D x² – 1 h(x) = log,(x +…

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: Find the indefinite integral of t/1+t

A: Here we have to find the indefinite integral of t/(1+t) .

Q: Compute the following values for the given function. h(s, t) = 2s ln(t) − 7t ln(s) h(1, e) =…

A: a) Given that s=1 and t=e  Then we plug the values in the formula and simplify

Q: b) Calculate the following definite integral: [* (√x - 1) dx

A:

Q: Choose the letter of the correct answe. 1) x² (xdy + ydx) = (5- xy) dx a) x ln (5-xy) = 1- cx b) -x…

A: We are allow to solve first question only .If you need rest of answer please upload it separately…

Q: Use the definition in terms of exponential functions to prove the following 1.tanh(In x) %3D x2+1

A:

Q: Q4. Find the integral of the following functions x dx (x-1)(x2+2x+1)

A:

Q: Evaluate J by means of Simpson's rule with n = 2m=10 and h = 0.10 = [*exp(-x²) dx Answer in 4…

A: f(x)=exp(-x2)h=b-an=1-010=0.10 table for x and y values x 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1…

Q: Evaluate the definite integral. e4 – x dx 14

A:

Q: Let f(x) = 9 · 5" ln(5). Find the most general antiderivative. F(x)

A:

Q: Evaluate the definite integral. 7e +1 '2 x e4x dx = 16

A:

Q: Determine for the following function: dy dx y = log3 (x² + 1) ○ (z²+1) In 3 2x O (1²+1) 2x O 2x…

A:

Q: Suppose F(x) = 19 dt. Find a formula for the function F(x4) expressed using an integral. e F(a*) = /

A: The given integral is F(x)=∫19xe-t2 dt

Q: dz +y ay dz 100 z= log ( x 100 + x50 y50 + y100 ), Prove that x

A:

Q: 3) Show that for any constants M, k, and a, the function k(t – a) y(t) : -M1+ tanh = 2 2 у satisfies…

A:

Q: Consider the conduction of heat in a rod 40 cm in length whose ends are maintained at 0°C for all t>…

A: Detailed explanation mentioned below

Q: Find for the following: dz y = ln O 2x+3 I O I 2x+3 3 21(2x+3) O In(+3) 2x+3

A:

Q: Find a value of x such that is equal to (a) ln 5 and (b) 1.

A:

Q: 1) Find dy/dt for if : y = log2 (81ln 2) 2) Evaluate the following integral In 2 * log2 (x + 2) dx x…

A:

Q: 3) Show that for any constants M, k, and a, the function k(t – a) y(t) M1+tanh 2 y' satisfies the…

A: To Show- Show that for any constants M, k, and a, the function yt = 12M1 + tanhkt - a2 satisfies the…

Q: (2) Differentiate the following w.r.t.x (i) cos (x + a²) (ii) ve+2) + 5 (iii) n log tan (iv) Vtan Vx

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: Consider the function. |1, 0<x< f(x) = 0, Sx < 1 Find the half-range cosine expansion of the given…

A:

Q: n²(ln(ar)) dr,a>0 J 2r In(ax) a.

A: