Concept explainers
In Exercises 3-6, compute the given derivatives with the help of formulas (1)-(4).
a.
b.
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CALCULUS+ITS APPL.,BRIEF-MYLAB MATH
- 2. a) Evaluate the following: -1 x-1(x+1)' xả-5x-20 x-5 x²-4x-5' x-5 i. lim ii. lim iii. lim- x-5x²-10x+25 √x²+4-2 x² 5h+4-2 iv. lim x-0 V. lim- h→0 h b) Find the derivative of the following functions: i. f(x) = -secx + 1 - secx ii. f(x) = x-5 tan 4x + sin 4x x iii. f(x) = ln(x-¹) [sinx + √x² + 1]. iv. f(t) = 3t² cost - t³ sin √t, e2x In(x²-3x+8) v. f(x) = (x+1)²arrow_forwardThe following is a step in the evaluation of the derivative of a function f(x) at a point x = 1 using First Principles. lim h→0 (3+h) ² - 9 h Which one of the following is the function f(x)? Select one alternative: ○ (x + 2)² ○ (x+3)² ○ 4x² - xarrow_forwardGiven selected value of the function f and its derivative in the table below, determine the value 4x - 2x² of lim x+2 f(2x) - 2x² in simplest form. f(x) f'(x) -2 7 10 5 -4 0 8 -4 5 7 9 0 8 X 1 2 3 Tarrow_forward
- Match the functions graphed in Exercise with the derivativesgraphed in the accompanying figures (a)–(d).arrow_forwardSOLVE STEP BY STEP IN DIGITAL FORMAT FIR W ジッッシ A A * U * ! ! ?? !! ? ?! & i !? X X X 2. Find the derivative of order two of the function h(x)=- 1-² 5-3x 8 & & & X♪ and simplify completely your answer.arrow_forwardDetermine f ″ ( x ) for f(x) = sec xarrow_forward
- Please help with part b)arrow_forwardQ1) Check the continuity of the given function at the given c (or c's). 2 if z+3 (a) f(=) = { -3 c= 3 5 if 1= 3 1+z if zS -2 (b) f(x) = { 2-z if -2 2 Q2) Find the derivative of each function. f). f(e} = In(sec8 + tan 8) 8) f(z) = In () „a) f(z) = %3D b) f(z) = sin %3D %3D 1+cosz c) f(z) = tsinz d) f(z) = (1+z)*(1 – 2)² h) y = (In(ax))² 1+conz g(z) = In(r³ – 3z + 2) i) ) iy = %3D e) f(z) = 19 – 16 +-4 Q3) 27-30 Differentiate f and find the domain of f. 7. f(x) = 28. F(x) = /2 + In x (I – x)u – 1 22. f(x) = In(x² – 2x) 30. (x) = In In In xarrow_forward(A) A = -2, B = -8 (D) A = 8, B = 2 f(x): = Let f RR be the function defined by : Ax³ + Bx + 2 Bx² - A if x ≤ 2 if x > 2. Find A and B so that the derivative of f is continu- ous on R. (B) A = -8, B = -2 (E) A = B = 2 (C) A = 2, B = 8arrow_forward
- From the text, the derivative of the function f(x) is f'(x) = lim h→0 following. lim h→0 f(x +h)-f(x) h lim h→0 lim h→0 8x 7x(x + h) h 7x(x + h) f(x+h)-f(x) h Substituting f(x) = 8 - into this formula and then writing the fractions with a common denominator, we have the 7xarrow_forwardpls answer d and earrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage