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CALCULUS EARLY TRANSCENDENTALS W/ WILE
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- What is the integral of the constant function f(x, y) = 5 over the rectangle [-2, 3] x [2, 4]?arrow_forwardShow that if f is differentiable and f'(x) > 0 on (a, b), then f is strictly increasing provided there is no subinterval (c, d) with c< d on which f' is identically zero.arrow_forwardLet a(t), 2 < t<8 be a positive function. Also, let the function 8(t) be defined as 8(t) = a'(t)/a(t) on the interval [2, 8]. Suppose that 8(t) 4/(t- 1), 2arrow_forwardFind the maximum value of of Iƒ" (x) [0,2] f(x)=√1+x² HINT: Much like the previous question except that you are focussing only on the max. Input your function as surd((1+x^2),2); Let your second derivative function equal abs(df2); assuming that df2 is the second derivative. Substitute your endpoints 0 and 2 into your absolute value second derivative function. Find third derivative and solve it for x. Substitute the result obtain into your second derivative absolute value function. Compare all y-values obtained for maximum value. 5) on the indicated interval. 6) Without the aid of a graph, find the absolute maximum and minimum values of the functionarrow_forwardLet f(x) = 6x2 on [1, 3.5]. (a) Find L(f, P) and U(f, P) when P = {1, 1.5, 2, 2.5, 3, 3.5}. (b) Use calculus to evaluate the integral 1 to 3.5 of 6x2 dxarrow_forward2. (Linearity of the integral) Let I= [a₁, b₁] x ... x [an, bn] be a generalized rectangle in R". Suppose that the function f: I→ R and g: I→ R are integrable, and a, 3 are real numbers. Prove that the function af + Bg: IR is integrable and Las (af * + 8g) = a[ƒ + B [ g. Show your argument step by step.arrow_forwardThe trapez rule is an approximation method to find approximate value (T, nɛN) of an definite integral (f (x)dx as follows: 1) h T. (S(x,)+2f(x)+2f(x,) +…· +2f(x,) + f(& - f(x,))= [f(x)dx. Here, a = x,, x = x, +k - h, k = 1,2,...,n, b-a h = Use Trapez rule to find approximate value of In(2) = | 2x -dx and fill the blanks in 1+x the Table below. (Note: Use a calculator and get 6 significiant digits after decimal point.) Absolute Relative Absolute True Approximate Approximate Error T, Error Error E, = In(2)–T,| E, = I×100% rnew 4 6 8 2.arrow_forwardstion 16 of 17 > Let P be the tangent plane to the graph of g(x, y) = 18 – 9x² – 18y at the point (4, 2, – 198). Let f(x, y) = 18 – x² – y. Find %3D the point on the graph of f where the tangent plane is parallel to P. (Use symbolic notation and fractions where needed. Give your answer in the form (*,*,*)). point: Question Source: Rogawski 4e Calculus Early Transcendentals Publisher: W.H. Freemanarrow_forwarda) 13/36b) 5/36c) 11/36d) 7/36arrow_forwardarrow_back_iosarrow_forward_ios
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,