lim (x' – 2x* +5)= x→-2 O a. 22 O b. -11 O C. -13 O d. -18

Q: Separate tanh-1(x+ iy) into real and imaginary parts.

A:

Q: [In(x²)-ex cos(x-1).tan(Tx) 20. lim 2x2-x sin2(1-x) X-1

A:

Q: What is the maximum value of y = cos x. For - < x < < ?? 1 1/2 2.

A:

Q: 2. Find the root of the function using Fixed-point Iteration. f (x) = x cos (x) - x?

A: Consider the given function as, fx=xcosx-x2

Q: |2tan x In (cos x) dx=

A:

Q: Use integration by parts to verify the reduction formula.

A:

Q: find the length of the curve y = arcsin e^(-x) from x = 0 to x = ln 5/4

A: Given curve, f(x)=arcsin e-x from x=0 to x=ln54

Q: 2tan x In (cos x) dx=

A: here we have to integrate the given integral.

Q: solve using reduction of order (D^2+1)y=tanx

A:

Q: Solve by Chain Rule y = tan ( V3x² + In(5X*))

A:

Q: Limit as x approaches 0 1-cos(x)/sin(x)

A:

Q: te dt lim 0 x-0 sin x =?

A:

Q: Using Differentials, approximate (4499)2-(401)2 AM

A: To approximate: 4.9992-4.012 Let, z=fx,y=x2-y2x0=5, y0=4 For the function z=f(x, y) at the point…

Q: Discuss the relationship between the derivative dy/dx and (Lim) with drawing if it is required ?

A: See the attachment

Q: If f(x) = x cosh æ + 3 sinh x then f'(x) =

A:

Q: limit x to 0 sin(4t)sec(1000t)/10t

A:

Q: If y = √√1-x² sin¹¹x, prove that (1-x²)+xy=1-x². dx

A:

Q: Find the length of the graph of f(x) = ln sec x from x = 0 to x = r/6.

A:

Q: tan (5x) x sin3 (2x) 2)- limx-o:

A: we have to evaluate the A=limx→0tan4(5x)xsin3(2x)

Q: If f(x) = x cosh x + 5 sinh x then f'(x) =

A: Find the derivative

Q: Solve without L'Hopital's rule. lim x→1 [tan(1 − x)] / (2x^2 + x − 3)

A: We have to find out limit

Q: Show that Costy+ Co5' (-x ) = TT.

A: To show that the given identity is true,

Q: aresin (2x-1) = 1-x 2 arctan

A: Substitute x = cos^2(theta) and simplify the equation.

Q: x-sinx 1. lim X-0 x-tanx

A: Given function is limx→0x-sinxx-tanx

Q: Lim as x approaches 0  1-cos(5x)+sin(3x)/x

A:

Q: )if x+tany+ sin-x+ In(yx) +3**1 =4 then find y'

A:

Q: y" + 2y' = sin 2x ||

A:

Q: find all possible functions with the givenderivative. y' = √θ - sec2 θ

A: Given: y'=dydθ=θ-sec2θ for evaluating solution of given differential equation, we use variable…

Q: 4) coth-lx = .In ( 1+x tanh-11 %3D 2 X-1,

A: i am solving question 4 for other question repost

Q: 4. Find the length of the arc of f(x) = ÷ (1+ x²)ē between x = 0 and x = 3. %3!

A:

Q: Find y' if y= In(tanhx) +cosh-(coth2x) Select one: O y' = cothx- 2csch2x 1 O y = -2csch2x sinh x…

A: The differential of products of trigonometric functions can be calculated using the product rule.…

Q: 1+ tanx y = logy 1- tanx prove that 9 = sec2x dy dx

A: Given,           y=log1+tanx1-tanx

Q: 3 tanh (In(4x)) sech" (In(4x)), I) y = tanh (In(4.x)) [y

A:

Q: ve of the function using the definition of derivative. = V7- x 1 2 7-x n of the function. (Enter…

A:

Q: 3. Prove that -2/3 dx diverges by showing that х lim -2/3 dx = 00 х

A: Given limit is Since one of the limit of integration is infinite , so we evaluate the limit as…

Q: Q3: Find value of x if 3 cosh x- sinh x= 4

A:

Q: ticle at time t assuming that x(0) = -1

A: The eigen vectors are : v1=-31 , v2=-71 The eigen values are : 7 and 5. The initial condition is…

Q: 2. Use the definition = f'(x) = limw-x- S(w)-r(x). to find the derivative of w-x y = tan x.

A:

Q: find the limit as x approaches 0. 12sin(3x)/1-cos(3x) = as x approaches 0

A:

Q: Using method of sub., find the Anti-derivative 1 x In x

A: detailed solution is given below

Q: 1: Find the derivatives of: 1+ tanh x a) y = In ソ= %3D 1- tanh x b) 2 y= cosh? 1-x? 1-x

A:

Q: Prove cosh 2 x - sinh 2  x =1

A: To prove  cosh2x-sinh2x=1

Q: how do you express lim,,→ Li=1 Σ! as п 1+ definite integral

A: We know that

Q: lim sin (xt3) dt X 5

A:

Q: Q2): If sinh(x) =find tanh(4x). %3D

A:

Q: Differentiate the functions showing the general process in determining the derivatives. Using the…

A: We need to differentiate given function.

Q: Find the partial derivative. xevllry ax

A: Given the function

Q: - S sech-x tanh x dx 1 2 2

A: From the given problem: I=∫sech12x tanh12x dx=∫sechx2 tanhx2 dx....1 As we know that:…

Q: 1 lim, „(e* + x)÷ +00

A: Explained below

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.