6. The function f (x) =cos (In x) exhibits two (2) local extrema and one inflection on the interval (0, 1]. Which of the following is the x-coordinate of the inflection? R. C. 7 In2 D. eln?

Q: 10. Approximate a value of z e [0,1] so that the length of the graph of f(x) tan(vx2 + 1) on [0,z]…

A:

Q: 1. Determine if g is differentiable at r 0 if 2 cos r, if -1<r <0 9(r) = if r20. r+cos r

A:

Q: 17. Find all values of the constants m and b for which the function [sin x, mr + b, 12T is a.…

A: Consider the give function y=sinx,          x&lt;πmx+b,      x≥π Since the function fx is continuous…

Q: 1. Determine the absolute extrema of f(x) = (sin r – 1) cos r on 2 2 if they exist, and identify the…

A:

Q: The function yow) satisfies the differantial equation x dy + ay Cos(xx) ak y(1) = 1 , the valu of…

A: Given differential equation is  xdydx+2y=cos(πx)x,y(1)=1

Q: Suppose z is a function of x and y. Solve for ∂z/∂y if tan √(y^2 + x^2 + z) = z^(x)e^(6y).

A:

Q: a2f b- For the following functions prove that ax2 ay2 1- f(x,y) = e-2y cos 2x %3D f(x,y) = In/x2 +…

A: The first step inludes the  partial differentiation of the functions individually with respect to y…

Q: ON REDMI Y3 AL CAMERA - veifhy coucly's is Theorem for the function C) 3 Cosh(z+2 where C is the…

A:

Q: One of the followings is a harmonic function O a. u(x,y)=(x' - y' – 2x+1), O b. u(x,y)=(x-y - 2x+1),…

A:

Q: 3 Use the definition 平grien FuncTionsEat'co,): for ー X+y X-ツ ix=ツ ) fory) =) singty4) ーty2 (x) #…

A:

Q: Let f(x) = cx + In(cos(x)). For what value of c is f'(T/4) = 5? %3D

A: Given: f(x)=cx+log(cos(x))  and f'π4=5 find values c

Q: Q1. If f(x.y,z) = cosh²(\x² In y) + tan-(ey*NE) + sec*(sin Vz In x²) Find fx, fy, fz fyx

A:

Q: The function f: x 1-> a + b cos x, is defined for 0sxs 2n. Given that f(0) = 10 and that %3D n)= 1,…

A:

Q: Suppose z is a function of x and y. Solve for dz if tan Vy? + x2 + z = z"e6y.

A:

Q: Given t2 -9 3 (2)f (=) = / dt 1+ cos (t) At what value of x does the local max of f(2) occur? %3D

A:

Q: If y = xsin then y is equal to = X" at x =

A:

Q: /hich of the following does not require the use of the dy nain rule to find ? dx A y = cos1 (10x –…

A:

Q: 1. Integrate the following functions over the given interval by using the extended trapezoidal rule…

A:

Q: For f(x): cos(x) + 2, choose all values of c in the interval TT 37 guaranteed by Rolle's Theorem. 2'…

A: Given, fx=cosx+2 f'x=-sinx By Rolle's theorem, fx=cosx+2 is defined in the interval -π2,3π2, such…

Q: az dz Find the and of the following function; ax ду (а)z %3D xln(ху) + уз, у3 сos(x? + 1) (b) z =…

A:

Q: 9. Show the function f(z) = 1 + 2i+2Re(z) is differentiable or not differentiable at any points.

A: Solution

Q: b- For the following functions prove that ax2 ay2 1- f(x,y) = e-2y cos 2x %3D 2- f(x,y) = Inx2 + y2…

A:

Q: 5) Find the following of the function f(x,y) =xy+cos y+ysin x

A: To find: The partial derivatives ∂2f∂x2,∂2f∂y2,∂2f∂x∂y. Given: The function is fx,y=x2y+cosy+ysinx.…

Q: 1. Find grad f for the given function below. Ax, y, z) = 5xy + 3yz – 4zx

A:

Q: 7. Find the value c that satisfies Rolle's Theorem for f(x) = cos x on A. T/2 В. "/4 C. 3/4 D. 0 Е.…

A: In this question we will use basic of calculus i.e concept of Rolle theorem. We will use Rolle…

Q: 1. Integrate the following functions over th given interval by using the extended trapezoidal rule…

A:

Q: Which of the following is a parameterization of the line that passes through the point (2, – 3) with…

A: Given, The line passing through the points 2, -3 with slope 4 We have to write the parameterization…

Q: The value of f(2) for the function f(x) = cos (x³) using forward finite difference with (h = 0. 15)…

A: The formula of the forward finite difference method is derived from the Taylor theorem. Substitute…

Q: 3. Suppose that {f(t)} = F(s) with F a differentiable function and that L{f'(t)} Exists. Then…

A:

Q: Let z be defined implicitly as a function of r and y by the equation dz 4+ In (ry) – cos (cy – 2) =…

A:

Q: on f(z) = e cos x+ ie-Y sin x is entire.

A:

Q: 3. For what value(s) of r on [0, 7] is the line tangent to the graph of f(x)= cos z horizontal? %3D

A:

Q: Let z be defined implicitly as a function of x and y by the equation dz 4+ In (xy²) – cos (xy – z) =…

A:

Q: In(x) Differentiate the function F(x) =| cos(e') dt (for x >0). 1/a Show and justify your work.

A: Given: F(x)=∫1xlnxcos(et)dt      (for x&gt;0) Leibniz rule states that…

Q: What is the period and domain of the function y=sec(x)? (2k + 1)T A Tn and xER | x = -, k is an…

A:

Q: 10. Find all the values of a in the interval [0, 27] such that f (a,=) - fxx (a,=) = 0 for f(x,y) =…

A:

Q: Suppose that function h (x) has antiderivative H (x) = 3 sin(x)+T. Which of the following are also…

A: The objective is to find the antiderivatives of h(x).

Q: 6. If f is continuous and f² f(x) dx = 6, evaluate S/² f (2 sin 0) cos de.

A: It is given that if f is continuous and ∫02f(x)dx =6 The objective is to evaluate ∫0π2f2Sin θcos θ…

Q: 22: Find dyldx for the following functions * (40 marks) · y = In (3 – 4 cos x) + (4x – 5)5 2. y = x²…

A:

Q: Q2. Let f(x) - In(cos x) (i) Find the are length (ds) of the function

A: Given,                f(x) = ln(cos x) ⇒y=ln(cos x) ⇒ dydx=-sin(x)cos(x). And we have to find arc…

Q: 5) Let y= cos' (S(x))+e". Find y' at x 1, given that f(1)= and f'(1) = 30

A: Given query is to find the derivative at indicated values.

Q: Analyze the approximate value and the exact value for (7.2, 4.06) for the function z = x3y2 sin(xy)…

A: Given below clear explanation

Q: 25. If f(x) = (cos x)*, then %3D is k-0

A:

Q: The function f : XI→ a + b cos x, is defined for 0 sxs 2n. Given that f(0) = 10 and that f (n) = 1 ,…

A: The range of a function is the values that can be obtained from the function by substituting all the…

Q: ()- 2y on [–10, 15]. Determine the absolute extrema of f (y) = sin

A: Here we have to find the absolute extrema.

Q: 5. Find Oz дz дх and if x - z = arctan(yz) defines z implicitly as a function of x and y. ду

A:

Q: Analyze the approximate value and the exact value for (7.2, 4.06) for the function z = x³y? sin(xy)…

A: Given below clear explanation

Q: 6. If x= sect and y=tant, evaluate at t =- of the following: dy (a) dx d'y (b) dx?

A: x = sect y = tant

Q: 4. Verify Rolle's theorem in the following cases (a) f(x) = (x – a)m (x – b)", where m and n are…

A:

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.