{"id":35106,"date":"2022-08-25T10:37:45","date_gmt":"2022-08-25T05:07:45","guid":{"rendered":"https:\/\/apboardsolutions.guru\/?p=35106"},"modified":"2022-08-25T10:37:53","modified_gmt":"2022-08-25T05:07:53","slug":"inter-1st-year-maths-1b-limits-and-continuity-solutions-ex-8e","status":"publish","type":"post","link":"https:\/\/apboardsolutions.guru\/inter-1st-year-maths-1b-limits-and-continuity-solutions-ex-8e\/","title":{"rendered":"Inter 1st Year Maths 1B Limits and Continuity Solutions Ex 8(e)"},"content":{"rendered":"

Practicing the Intermediate 1st Year Maths 1B Textbook Solutions<\/a> Inter 1st Year Maths 1B Limits and Continuity Solutions Exercise 8(e) will help students to clear their doubts quickly.<\/p>\n

Intermediate 1st Year Maths 1B Limits and Continuity Solutions Exercise 8(e)<\/h2>\n

I.<\/span><\/p>\n

Question 1.
\nIs the function f, defined by \\(f(x)=\\left\\{\\begin{array}{l}
\nx^{2} \\text { if } x \\leq 1 \\\\
\nx \\text { if } x>1
\n\\end{array}\\right.\\) continuous on R?
\nSolution:
\n\"Inter
\nf is continuous at x = 1
\nf is continuous on R.<\/p>\n

Question 2.
\nIs f defined by f(x) = \\(=\\left\\{\\begin{array}{cc}
\n\\frac{\\sin 2 x}{x}, & \\text { if } x \\neq 0 \\\\
\n1 & \\text { if } x=0
\n\\end{array}\\right.\\) continuous at 0?
\nSolution:
\n\"Inter
\nf is not continuous at 0<\/p>\n

\"Inter<\/p>\n

Question 3.
\nShow that the function f(x) = [cos (x10<\/sup> + 1)]1\/3<\/sup>, x \u2208 R is a continuous function.
\nSolution:
\nWe know that cos x is continuous for every x \u2208 R
\n\u2234 The given function f(x) is continuous for every x \u2208 R.<\/p>\n

II.<\/span><\/p>\n

Question 1.
\nCheck the continuity of the following function at 2.
\n\"Inter
\nSolution:
\n\"Inter
\nf(x) is not continuous at 2.<\/p>\n

Question 2.
\nCheck the continuity of f given by f(x) = \\(\\begin{cases}\\frac{\\left[x^{2}-9\\right]}{\\left[x^{2}-2 x-3\\right]} & \\text { if } 0<x<5 \\text { and } x \\neq 3 \\\\ 1.5 & \\text { if } x=3\\end{cases}\\) at the point 3.
\nSolution:
\n\"Inter
\nf(x) is continuous at x = 3.<\/p>\n

Question 3.
\nShow that f, given by f(x) = \\(\\frac{x-|x|}{x}\\) (x \u2260 0) is continuous on R – {0}.
\nSolution:
\nCase (i) : a > 0 \u21d2 |a| = a
\n\"Inter
\n\"Inter<\/p>\n

If x = 0, f(a) is not defined
\nf(x) is not continuous at \u20190′
\n\u2234 f(x) is continuous on R – {0}<\/p>\n

\"Inter<\/p>\n

Question 4.
\nIf f is a function defined by
\n\"Inter
\nthen discuss the continuity of f.
\nSolution:
\nCase (i) : x = 1
\n\"Inter
\nf(x) is not continuous at x > 1<\/p>\n

Case (ii) : x = -2
\n\"Inter
\nf(x) is not continuous at x = -2.<\/p>\n

Question 5.
\nIf f is given by f(x) = \\(=\\left\\{\\begin{array}{cl}
\nk^{2} x-k & \\text { if } x \\geq 1 \\\\
\n2 & \\text { if } x<1
\n\\end{array}\\right.\\) is a continuous function on R, then find the values of k.
\nSolution:
\n\"Inter
\n2 = k\u00b2 – k
\nk\u00b2 – k – 2 = 0
\n(k – 2) (k + 1) = 0
\nk = 2 or – 1<\/p>\n

Question 6.
\nProve that the functions ‘sin x’ and ‘cos x\u2019 are continuous on R.
\nSolution:
\ni) Let a \u2208 R
\n\"Inter
\n\u2234 f is continuous at a.<\/p>\n

ii) Let a \u2208 R
\n\"Inter
\n\u2234 f is continuous at a.<\/p>\n

III.<\/span><\/p>\n

Question 1.
\nCheck the continuity of ‘f given by
\n\"Inter
\nat the points 0, 1 and 2.
\nSolution:
\ni) \"Inter
\n\u2234 f(x) is continuous at x = 0<\/p>\n

ii) \"Inter
\n\u2234 f(x) is continuous at x = 1<\/p>\n

iii) \"Inter
\n\u2234 f(x) is continuous at x = 2<\/p>\n

\"Inter<\/p>\n

Question 2.
\nFind real constant a, b so that the function f given by
\n\"Inter
\nis continuous on R.
\nSolution:
\n\"Inter
\nSince f(x) is continuous on R
\nLHS = RHS \u21d2 a = 0
\n\"Inter
\nSince f(x) is continuous on R.
\nLHS = RHS
\n3b + 3 = -3
\n3b = – 6 \u21d2 b = -2<\/p>\n

Question 3.
\nShow that
\n\"Inter
\nwhere a and b are real constants, is continuous at 0.
\nSolution:
\n\"Inter
\n\u2234 f(x) is continuous at x = 0<\/p>\n","protected":false},"excerpt":{"rendered":"

Practicing the Intermediate 1st Year Maths 1B Textbook Solutions Inter 1st Year Maths 1B Limits and Continuity Solutions Exercise 8(e) will help students to clear their doubts quickly. Intermediate 1st Year Maths 1B Limits and Continuity Solutions Exercise 8(e) I. Question 1. Is the function f, defined by continuous on R? Solution: f is continuous …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[15],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/35106"}],"collection":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/comments?post=35106"}],"version-history":[{"count":1,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/35106\/revisions"}],"predecessor-version":[{"id":35107,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/35106\/revisions\/35107"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/media?parent=35106"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/categories?post=35106"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/tags?post=35106"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}