[B] If Z = 4 cos w – bw, find the relative percentage error in Z at w = 0, if the error in w = 0.005. -

Q: Find the average rate of change of the function over the given interval. f(t) = 13 + cos t a. - T, 2…

A: given f(t)=13+cos(t) To find the average rate of change of f(t)

Q: dy For the function dt 5 cos t, the third order derivative dt is O 5 cost O 5 sint O -5 sint O -5…

A: Given  dydt=5 cos t          ............ (1) We have to calculate the third-order derivative of y…

Q: 1 R(t) = 2 sin(t) – 4 cos(1)

A:

Q: Find the correct estimation of the value tan-1(2) by using Simpson's Rule with n = 4. A.) 1.1384 B.)…

A: Simpson's 1/3 rule ∫abf(x)dx≈h3(f(x0)+4f(x1)+2f(x2)+4f(x3)+2f(x3)+ ⋯ ⋯…

Q: Given f(t) 1 + cos² (x) At what value of t does the local max of f(t) occur? t = C 4 x² + 11x + 28…

A:

Q: Find for the following function: dx 1- y = sin-1 V2x + 3 2- y = 3cot(cosx) 3- v = r?y at r = 1

A: AS PER GUIDELINE WE HAVE TO SOLVE THREE SUBPARTS

Q: Use the total differential to find the slopes of the indiffa of the following utility functions: a)…

A: a) slopes of the indifference of the following utility functions  ux1,x2=x1x2 mux1=dux1,x2dx1=x2…

Q: 7n Find the average rate of change of f from t to 2 f(x) = cos 2 %3D

A: The average rate of change of the function is:

Q: Which function is equivalent to f(t) = cos 4(t- T1/4)? *

A: Given that  f(t)=cos4(t-π\2)we need to find the equivalent equation from the given equation

Q: For the function f(x,y)= (x² + y²) tan(ln(xy)) + e(x-y) which of the following is the value of…

A:

Q: Which of the following functions listed below will result in differentiating f(r) = cosh(r) +e a…

A: Option A is correct.  If we differentiate for the first time we get f'(x) = sinhx - e^(-x)  Again…

Q: The derivative of a^u with respect to x is a ln a du/dx (a^u) * du/dx ln a * du/dx (a^u) * ln a *…

A:

Q: COS Z fined the Res of the function T Z 4 -

A:

Q: Find the given higher-order derivative. f (4)(t) = t cos t, f (5)(t)

A:

Q: Use the Product Rule to compute the derivative: d. Find dt (e + 1)(t + 9)) at t = 13

A: Topic :- Derivative

Q: cos='A F'A where A =atib

A:

Q: Consider the following function and express the relationship between a small change in x and the…

A: Givenf(x)=10-acosxwhere a is constant

Q: of dx- = 0, then dy |=0. Prove that is a function f is harmonic

A:

Q: 2x g(x) = |VI+t? dt 1+t2 dt %D

A: To find the derivative

Q: Given f(r) = z - sin z, determine all values of z in (0, 27) where f(x) has a horizontal tangent.

A:

Q: Find the derivative (dy/dx) of the following functions: h) у%3D Зx7 —7х3 + 21x2 - i) y = (x² +…

A: Since you have asked multiple questions in a single request, we will be answering only the first…

Q: Calculate the error of approximation with EA for the following functions TC f(x = 4 cos 5x when x =…

A: We know: lim∆x→0∆y∆x = dydx…

Q: Find the most general antiderivative of the following functions. (d).r(θ) = (sec θ − tan θ)^2

A:

Q: e' cos x = 1 + sin(xy

A:

Q: Given f(æ) = / - t2 + 2t – 35 -dt 1+ cos?(t) - At what value of x does the local max of f (x) occur?…

A:

Q: Find for THREE of the following functions: dx 1-y()+In(cos(x)) + √2-y=2(cos(x))*(x)

A:

Q: The derivative dy for the function %3D (1i) y= cot リーCof V-x

A:

Q: Find for the following function. dx y = 3 cos x sin x dx II

A: Take derivative on both sides Take the constant 3 out from the function ,

Q: Use an appropriate local linear approximation to estimate the value of the given quantity. Round…

A:

Q: Given f(x) cos r, determine all values of x in [0, 27) where f(x) has a horizontal tangent.

A: We have to find the value of x

Q: Find f(x), where f'(x) = sin(x) + cos(x) + 1 and f(T) = 2.

A:

Q: For the given function f(x) = cosx, let xo = 0, %3D X1 = 0.5, and x2 = 0.7. Find the value of…

A: From the given x=0.75, x0=0, x1=0.5 and x2=0.7. It is known that, the lagrange interplotation…

Q: Given f(x) = x + sinx, determine all values of x in [0, 2π) where f(x) has a horizontal tangent. x =

A:

Q: for the function f(x) = 2 cos(45x)o , determine:  the average rate of change for the interval 13  ≤…

A:

Q: Find f(x), where f'(x) = sin(x) + cos(x) +1 and f(T) = 2.

A: We have to find

Q: Given f(m) = | | 1+ cos°(?) t2-49 dt At what value of x does the local max of f(x) occur?

A:

Q: Given f(x) = + sin z, determine all values of x in [0, 27) where f(x) has a horizontal tangent. x=

A:

Q: Given F(x) below, find F'(x). cos (x) F(x) = (1² + 10) dt 3

A:

Q: Given that (1 COS 4.r) x2 a, if x = 0 if x 0. J 16+ Vx -4 If f(x) is continuous at x = 0, find the…

A:

Q: Find the second of the finchion, ç x) = cos e derivative f (x) (x %3D %3D

A: Consider the given function: f(x)=xcosx The first derivative is calculated using the product rule.…

Q: Find the first order derivative for the following: cot(e(3•Z)t) sin(z•t²) S = t5

A:

Q: Given f(x) = , 1+ cos²(t) t? - 9 dt %3D 0. At what value of x does the local max of f(x) occur?

A:

Q: Given that f (x, y) = y ln x cos x, find fæærzay (T, 1). Keep your answer to three significant…

A:

Q: Find for the following function. dx y=9 cos x sin x dy

A: Differentiate y with respect to x using product rule.

Q: Calculate the error of approximation with Ea for the following functions when x = 2, Ax = dx = 0.08

A: If the input of a function y=f(x) changes, its output also changes. The derivative of a function is…

Q: Find the linearization of the following functions at x=0. a) sin x L(x)= x b) cos x L(x)= 1 c) tan x…

A: As per guideline we have to solve only three

Q: a² f For the function ƒ(x,y), compute Or d0 if x =r cos O and x=r sin 0 .

A:

Q: Use an appropriate local linear approximation to estimate the value of the given quantity. Round…

A: cos32° It can be written as, cos32°=cos30°+2° Now, fx=cosx, x=30° & ∆x=2°=2π180 radians Now…

Q: Which of the following is the slope of the tangent line to f(x) = cos(ax), a E R at x = T? 1 а 1 а

A: Given equation is f(x)=cos(ax) at x=π Find the slope of the tangent line

Q: What is the derivative of r(t)=e^(4t)costi+e^(4t)sintj+e^(4t)k

A: Differentiate both sides with respect to t.

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.