I need help with this one, I am not understanding at all. Please only use the formulas on the sheet that I have provided. Similarly, please write it so that I can read it! 1. Set up the difference quotient for the following derivatives, then calculate the limit without using any derivative rules.a. f(x)=√x + 2, at a = 7.b. s(t) =2-, at a = x.3-tc. h(x) = x² + 2x + 5, at a = − 1. MULTIPLE DERIVATIVESA function fis-times differentiable (or fE C") if you can applythe derivative times to fand have a continuous function aftereach application of the derivative.A function fis smooth (orf E C) if it can be differentiatedinfinitely many times, and each derivative is a continuousfunctionLinearity:Products:Quotients:Compositions:DERIVATIVE PROPERTIESd[f(x) + a· g(x)] = f(x) + a · g(x)dxddx[ƒ(x)g (x)] = f(x)g (x) + f(x)g'(x)d f(x)dx [g(x)]ddxf(x)g(x) = f(x)g'(x)(g(x)) ²where g(x) = 0[ƒ (g(x))] = f(g(x)) · g'(x)TANGENT AND NORMAL LINESIf y=f(x) describes some differentiable function, the equation ofthe tangent line at a pointis given byy = f(x)(x − a) + f(a).The equation of the normal line at a point(x-a) + f(a).If fis differentiable nearf (a)is given byLINEAR APPROXIMATIONthen for values close to,f(x) = f(a)(x-a) + f(a).Constant:Power:Exponential:Logarithmic:BASIC FUNCTION DERIVATIVESTrigonometric:Hyperbolic:ddxddxddxddxddxdd[b] = ln(b) b*, where b € (0,0)dxddx[a] = 0, where addxMdxddxddxInverse Trigonometric:ddxddxddx=x²-¹, where[log(x)] =[sin(x)] = cos(x)[cos(x)]=sin(x)[tan(x)] = sec²(x)[sec(x)] = sec(x)tan(x)[cot(x)]=-csc²(x)[csc(x)]=csc(x)cot(x)[arcsin(x)][arccos(x)]In(b) x[arctan(x)]1+x²where b, x € (0,00)[sinh(x)] = cosh(x)[cosh(x)] = sinh(x)where x = ±where x ±CZOOM +

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1. Set up the difference quotient for the following derivatives, then calculate the limit without using any derivative rules. a. f(x)=√x + 2, at a = 7. b. s(t) = 2 -, at a = x. 3-t c. h(x) = x² + 2x + 5, at a = − 1.

1. Set up the difference quotient for the following derivatives, then calculate the limit without using any derivative rules. a. f(x)=√x + 2, at a = 7. b. s(t) = 2 -, at a = x. 3-t c. h(x) = x² + 2x + 5, at a = − 1.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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