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Уважаемые эксперты, добрый день! Если можите, помогите решить мне следующие задания: 1) Применив формулу Тейлора с остаточным членом в форме Лангранжа к функции f(x)=e в степени х, вычислить с точностью до 0,001 значения, е в степени а и е в степени b . Методом линейной интерполяции вычислить приближенного значение е в степени х нулевое. Если дано; a=0,31, b=0,34, x нулевое=0,32.
2) Найти наибольшее и наименьшее значения функции y=f(x) на отрезке [a,b]. если; f(x)=1/2*x+cosx, [-3/2*pi, -pi]
3) Исследовать методами дифференциального исчисления функции и построить ее график, используя результаты исследования. Если; y=x в кубе делить на, 2*(х+1) в квадрате.
4) Найти уравнение касательной и уравнение нормальной плоскости линии r = r(t) в точке t нулевое . Если; r штрих сверху(t)= (t в четвертой - 3t в квадрате)*i штрих сверху + (t в кубе + 2t)*j штрих сверху + (4/t)*k штрих сверху; t нулевое= -1
5) Дана функция z=f(x, y) и две точки А(х0 , y0) и В (х1, y1). Требуется: 1) вычислить значение z1функции в точке В; 2) вычислить приближенное значение z1 функции в точке В исходя из значения z0 функции в точке А, заменив приращение функции при переходе от точки А к точке В дифференциалом; оценить в процентах относительную погрешность, возникающую при замене приращения функции ее дифференциалом; 3) составить уравнение касательной плоскости к поверхности z=f(x, y) в точке С (x0, y0, z0). если; z=xy+2x-y, A(2, 2), B(1,39, 2,05).
6) Найти наибольшее и наименьшее значения функции в замкнутой области. Если; z=1/2*(x в квадрате) - xy в области, ограниченной параболой y=1/3*(x в квадрате) и прямой y=3.
7) Дана функция z=z(x, y), точка A(x0, y0) и вектор а. Найти: 1) grad z в точке А; 2) производную в точке А в направлении вектора а. Если; z=3x/(y в квадрате), A(3, 4), a= -3i - 4j.
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