Indicate if the following function increase or decrease at given interval: f(x) = 3x² + 2 cos(x), х€ [11,20] f(x) = 2x + 5 ln(3**), xe[11,20] 2x f(x) = 5x3. хе [11,20] %3D - х — 10х2'

Q: The derivative of f(z) = Log(2iz – 4 + 6i) at z = -3 + 4i is %3D Log(-12). O 2i -12 None of them O…

A: We have to find Derivative using definition and L'Hospital Rule.

Q: a if y = In (sinh 50) and x = 7. cosh 40

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A:

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A:

Q: Solve Cauchy Euler DE 4x^2y"-4xy'+3y=sin ln(-x), x less than 0

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A:

Q: Suppose that the cost of producing x apple is c(x) = 2000 + 100x - 0.1x^2. Find the function f(x)…

A: We will find out the required function.

Q: (A) Ln(2) S Sinh(x) Cosh² (x) dx

A:

Q: у (4) %— Зх3 8 e x7

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Q: 5. Calculate the derivatives of sinh¬1x, cosh¬1 x, and tanh¬ x. Hence, express each of the…

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A:

Q: 4)* Find the derivative of f(x)= Arcsecr. %3D f'(x) = 4 rv.r* O None of the above O Option 4 f"(x)=:…

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Q: The derivative with respect to x of the function y = 3tan ¹x - y' = cotx O the above (In 3) log3…

A: Given y=3tan-1x-ln3log3cosecx

Q: Find

A:

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A:

Q: Show that In(x") = y In(x) for all x, y > 0, only using the rules of derivative for the natural…

A:

Q: Compute backward difference approximations for the first derivative of the function, y = log(x? +…

A: Given is the function y=log(x2+1)2   .  It is needed to compute backward difference approximation…

Q: Use one or more logarithm identities to show that In (2) In(x) for any > Use one or more logarithm…

A: we have to do as per the question.

Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Given :             cosh(3x2y) = x + ln(exy + 1)   To find :            ∂y∂x

Q: The derivative of the function y = 9 sin + 22 is. 0 + (In 2") O - (In 2)2= O + (In 2)2" 0로+ (In 2)2"…

A:

Q: 31. Verify the formulas sinh-x = In |x + Vx² + 1| coshx = In |x +Vx² – 1| (for x > 1)

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: logtan nx(2+ 4 cos nx) 2

A:

Q: Use forward-difference formula to evaluate the first derivative of y = cos(x) at x = cos(x) at x =…

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Q: Differentiate the function:  k(x) = 4 ln (x) + 2 cos x + x^2 k'(x) =

A: k(x)=4ln(x)+2cosx+x2Differentiate with respect to xk'(x)=(4×1x)+2-sinx+2xk'(x)=4x-2sinx+2x

Q: Solve for x in the interval 0 < x < 2n. log (sin (x)) – log (cos (x)) = 0 a) x = 5,

A:

Q: i. Show with the aid of Argand Diagram, where Ln(z³ + 3) is analytic . ii. Determine the derivative…

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Q: 2 Compute the derivative f'(x) of the logistic sigmoi 1 f (x) : 1+ exp(-x)

A: We have to find

Q: Show that (1+:)'→e. as x → o, → e. HINT: Since the logarithm function has derivative 1 at x = 1, %3D…

A:

Q: Find dx 1- y = log (Sin x )- Cot - Vx 3 2. y = log( vx) = tan(x - y) 3- x Sec -x = y? log (sec x) 4-…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the linearizationsof the following functions at x = 0. ln (1 + x)

A:

Q: Compute backward difference approximations for the first derivative of the function, y = log(x² +…

A: We have to compute backward difference approximations for the first derivative of the function,…

Q: If f(x)-logCos4x + sinx.Then find 9 (x) JP at x= sec 2c dx 6.

A: Given function is: f(x)=logsec2x|cos4x|+|sinx| To find the value of 9df(x)dx at x=-π6

Q: 2. Use the identity of inverse hyperbolic function to solve cosh-(2 – a2) = ln 2, for |æ| < 1.

A:

Q: 4. Find all derivatives of f(x) = x*, where k is some unknown natural number.

A: f(x) = xk and we need to find all the derivatives of f(x)

Q: Estimate cos(x²)dx by using a right-hand sum and 4 subintervals. |cos(x²)

A:

Q: Find the derivative y = 2* log3 x xln3 2* log3 x + xln3 (In x) · In 2 In 3 + n 32 x-In 3 None of…

A: At firts apply base change formula for log3x. Base change formula is logba= logea/logeb. Then find…

Q: Find the derivative of y. x2 =log6 x+1 O A) Sx+1 x2 O B) ) In 6 x2 2x+1 1 Sx+1 In 6 x2 D) None of…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3. Find the first derivative of the function f(x)= 2x3-4x+1 using forward Difference formula if, X1…

A: Solution:

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: = 1. Use a local linear approximation of the function f(x) = ln(x + sinh(x) + cosh(x)) at some point…

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Q: dx =?

A: we have to solve integration

Q: 1.) Find the area under the curve y = x3 + 3x2 and the axis between x = 1 and x = 3.

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Q: Consider the function g defined by 1 g(x, y) = cos (7x/) - CoS log3(x – y)

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Q: 8. (a) Evaluate the indefinite integral dx sinhx+coshx e 4x (b) Find and simplify the derivative of…

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Q: If g(x) : 8 + cosh(9x) find g'(x) 8+ cosh(0)

A: Answer and explanation is given below

Q: 3. Jメニ

A: We can find the antiderivative as below

Q: Definite integrals Evaluate the following definite integrals. Use Theorem 7.7 to express your answer…

A: Evaluate: ∫-22dtt2-9